Instructions (read carefully!)
Mandatory Requirements
Grading Criteria
Problem 1
- Reading Data set Healthcare
Data Exploration
- Summary gives us the values of the min, 1st quantiles, median, mean, 3rd quantiles and max values of each variable on a graph of each variable.
Dplyr data explorations
- Here I added a new column or variable called finalcosts where I added the the previous balance and the costs column together to make the finalcost column using mutate function.
- Body mass increase with final cost ( prev_balance + costs). I also factored in the graph to divide the smokers in blue and non smokers in red. Here you can see that non smokers are paying less for healthcare and smokers are paying a lot more around 25K-50K for healthcare cost. Insurance companies would have to charge smokers more in healthcare cost.
- Here are the first 6 rows of the most significant variables in the healthcare dataset with the lowest p values in the data set. I listed the first 6 rows to exam the data set since printing all rows would take up too much space. Here you can see that a 63 yrs old person with a body mass index of 36.7 pays less healthcare cost compared to an 18 year old smoker with a body mass of 42. Just by looking at those two patients you can see that these variable are very significant to the cost of healthcare.
- The arrange function arranges all the column from least to the most.
People paying the most for healthcare costs are mostly smokers, people with negative prev_balances and are females with 4-3 or 0 children live in southwest, northeast, southeast.
Linear Regression model for Healthcare dataset where test all variables against costs except for the previous balance varoable
1. Here is a linear regression model where we use all variables except previous balance.
- Linear Regression on all the features or variables in the Healthcare data set
- Box plot graphs of previous balance column vs costs
  - Looks like the pre_balance variable has a parabola with prices owed and owed to them spreading out from zero to the positive and negative evenly.
- Scatter plot of age vs costs
- Histogtam of the amount of patients at different age groups
- Histogram of number of people at different BMI
- Histogram of the number of people paying different costs for healthcare in the dataset
- Histogram of the amount of people that carried a range of previous balance for healthcare.
- Histogram of number of patients with 0-5 children in thier family.
- Boxplot of patients from different regions vs the costs of healthcare
  - Looks like we have people in southeast paying more for healthcare. The other regions look very close to each other with southwest a little lower in healthcare cost.
- Scatter plot showing healthcare cost increases with BMI, vs regions vs gender
  - Healthcare cost increases with body masss. The male blue line shows that males under twenty pay less for healthcare and after age 23 they start paying the same as females for healthcare. But when males reach their 30’s they start paying more for healthcare cost compated to females. This scatter graph it is difficult to determine where people live determines the healthcare cost.
  - looks like male and female both increase their healthcare cost as they have children. It seems like males pay a litte more if they grow their family. The region location of patiensts is hard to read in this graph. But seem like more southeast outliers paying 40K-60K
- Scatter plot of BMI vs gender and region
Scatterplot heat map
- Doesn’t look like there is a correlation. Most people do seem to have a previous balance of zero.
- The male blue line shows that males under twenty pay less for healthcare and after age 23 they start paying the same as females for healthcare. But when males reach their 30’s they start paying more for healthcare cost compated to females.
- Linear Regression on all the features or variables in the Healthcare data set
- Linear Regression on all the features or variables except gender in the Healthcare data set
- Linear Regression the features of body mass in the Healthcare data set vs costs.
- Mean Residuals for the Linear regression ran above.
- RMSE Root Mean Square Error
Here we will split our Healthcare dataset in to a Training and Testing set to test out our Linear regression model and see if we can train our model and test it to see how accuarte it can predict the cost of healthcare.
- Spliting Data into train and test set with caTools
  - Here we set a seed so the training set and test set can be reproducible. Otherwise it would be random and we can’t reproduce the data for practice.
- Residual plot to determine the random noise of the model
  - Looks like the residuals are not distribued normally. There is some weird pattern and the correlation not accounted for. So this might be bad example of residual distribution. Maybe linear regression is not the best model for this data set to predict the cost of healthcare. ( there was an issue with running this augment and I commented it out)
- Scatterplot looking at the BMI vs Cost and filtering the outliers with body mass greater than 35
- Calculating the Residual Mean
  - plot out the residuals:
Classification and Regression Tree model for the Healthcare data set to determine cost of healthcare.
- Tree model maybe a better model to predict and determine the cost of healthcare.
  - Model interpretability is makes predictions easier in Tree Classification
  - Model performance of trees have superior performance compared to other ML algorithm.
- Here we look at how smokers effect on the price of healthcare cost.
- Here we look at the different region of patients paying for healthcare costs.
- Here is a classification on region an body mass.
- This Regression tree is looking at the Age of the patients in the model.
- This Regression tree is looking at the BMI of the patients in the model.
- This Regression tree is looking at the number of children patient’s have in the model.
- This Regression tree is looking at the previous balance of the patients in the model.
how many rows are in the data
Follow down the Tree:
Slit to Training/Testing/Validation with three sets for Regression Tree
Training with Regression Tree
Predict the cost for all the people in the test set Evaluate model based on test set RMSE Room Mean Square Error.RMSE tells us approximately how far away our predictions are from the true values
Tuning model: Tune model using prune() function by finding best ‘CP’ complexity parameter
Generate grid of hyperparameter values uinge expand.grid() to generate grid of maxdepth and minsplit values
Generate grid models
Evaluate the grid
- After the Hyperparameter the best fit model for the Regression tree Predicts that the predicted cost for Healthcare is $3910.80
Problem 2
glycohemoglobin % above 6.5 your prediabetic
Train Test split
Random Forest
Train Test split
Random Forest model
- Random forest Visualization
Gradient Boosting Machine (GBM) algorithm

Instructions (read carefully!)

Use this R Markdown .Rmd file to complete your project
- Change the author to your name above.
- Rename this file to challenge_problems_ your last first name.Rmd (of course, substitute YOUR last_name_first_name!)
- Submit both your knitted .html file and R Markdown .Rmd file to Canvas assignment Challenge Problem.
- No email submissions will be accepted submit to Canvas only (I will dock points for this!)
- Due: December 12, 2018, 6:30 PM. Because of UCB grading requirements, no late submissions will be accepted.
- Make sure you leave extra time to submit your assignment in case you run into problems. I will grade your final submission.

Mandatory Requirements

Do your own work. No sharing code, no sharing R Markdown text.
Use only concepts, topics, and packages covered in class (zero credit otherwise).
Everything you submit should be contained in this .Rmd file, data files assumed to be in the same directory. I should be able to download it on to my computer and click “Knit” in Rstudio to generate your submitted .html results. Non-reproducible submissions will result in no credit.
Use tidyverse (e.g., ggplot) packages and tidy approaches in place of base R when possible and appropriate.
Use consistent and accepted R style: meaningful variable names, snake_case_variable_names, properly indented code in code chunks
Your final knitted .html product should be clear, readable, and even understandable to an outside reader.
Use glimpse() and/or head() to show results. Do not show long printouts of data or results (points will be deducted for this)
Organize your code into readable code chunks. Points will be deducted for excessively long code chunks.
Put analysis in R Markdown text, use code comments to clarify code only, use R Markdown text for explanations!
If you have any questions, please contact me individually by email.

Grading Criteria

Think of this as the type of challenge problem typically given to a Data Scientist/Analyst job candidate.
Whether your product tells a coherent story about the data + problem
Completeness
Clarity of code and explanations
Correctness of code and explanations
Important: follow Mandatory Requirements described above!

Problem 1

Use the dataset healthcare data frame (see below) to fit
- an OLSR linear (lm) model
- a CART (rpart) model
to predict costs
Explore the dataset as needed to guide your analysis
Prepare your dataset (e.g., to avoid overfitting)
Fit your models using lm and rpart
Tune your models to optimize performance
Show and explain your results, use plots where appropriate
Evaluate model performance
State your conclusions

Use only Ordinary Least Sum Regression (lm) and Classification Regression Tree (rpart) models; do not use caret in Problem 1

Reading Data set Healthcare

#  Do not change the code in this chunk!
healthcare <- read_csv('healthcare.csv')

Data Exploration

library(tidyverse)
library(dplyr)
library(broom)
glimpse(healthcare)

Observations: 1,338
Variables: 8
$ age_yrs      <dbl> 18, 43, 62, 49, 46, 63, 41, 55, 52, 25, 62, 48, 19,…
$ gender       <chr> "female", "female", "male", "female", "male", "male…
$ body_mass    <dbl> 42.240, 30.685, 37.400, 23.180, 40.375, 36.765, 33.…
$ no_children  <dbl> 0, 2, 0, 2, 2, 0, 3, 2, 0, 0, 0, 0, 1, 5, 2, 0, 1, …
$ smoker       <chr> "yes", "no", "no", "no", "no", "no", "no", "no", "n…
$ region       <chr> "southeast", "northwest", "southwest", "northwest",…
$ prev_balance <dbl> -17938.42104, 195.25679, -4272.92335, 1480.08209, -…
$ costs        <dbl> 38792.686, 8310.839, 12979.358, 10156.783, 8733.229…

###Here are the list of Variables in the data set Healthcare

Summary gives us the values of the min, 1st quantiles, median, mean, 3rd quantiles and max values of each variable on a graph of each variable.

Describe give us the general discription of our variable, min max, mean, range. It is good to use these function to understand our data during the data explorations.

library(psych)


Attaching package: 'psych'

The following objects are masked from 'package:ggplot2':

    %+%, alpha

describe(healthcare)

Warning in describe(healthcare): NAs introduced by coercion

Warning in describe(healthcare): NAs introduced by coercion

Warning in describe(healthcare): NAs introduced by coercion

Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
Inf

Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
Inf

Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
Inf

Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
-Inf

Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
-Inf

Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
-Inf

             vars    n     mean       sd  median  trimmed     mad
age_yrs         1 1338    39.21    14.05   39.00    39.01   17.79
gender*         2 1338      NaN       NA      NA      NaN      NA
body_mass       3 1338    30.66     6.10   30.40    30.50    6.20
no_children     4 1338     1.09     1.21    1.00     0.94    1.48
smoker*         5 1338      NaN       NA      NA      NaN      NA
region*         6 1338      NaN       NA      NA      NaN      NA
prev_balance    7 1338   136.09  4600.38  -13.35    40.42 2079.79
costs           8 1338 13270.42 12110.01 9382.03 11076.02 7440.81
                   min      max    range skew kurtosis     se
age_yrs          18.00    64.00    46.00 0.06    -1.25   0.38
gender*            Inf     -Inf     -Inf   NA       NA     NA
body_mass        15.96    53.13    37.17 0.28    -0.06   0.17
no_children       0.00     5.00     5.00 0.94     0.19   0.03
smoker*            Inf     -Inf     -Inf   NA       NA     NA
region*            Inf     -Inf     -Inf   NA       NA     NA
prev_balance -27607.54 30313.76 57921.30 0.60     9.07 125.77
costs          1121.87 63770.43 62648.55 1.51     1.59 331.07

summary(healthcare)

    age_yrs         gender            body_mass      no_children   
 Min.   :18.00   Length:1338        Min.   :15.96   Min.   :0.000  
 1st Qu.:27.00   Class :character   1st Qu.:26.30   1st Qu.:0.000  
 Median :39.00   Mode  :character   Median :30.40   Median :1.000  
 Mean   :39.21                      Mean   :30.66   Mean   :1.095  
 3rd Qu.:51.00                      3rd Qu.:34.69   3rd Qu.:2.000  
 Max.   :64.00                      Max.   :53.13   Max.   :5.000  
    smoker             region           prev_balance           costs      
 Length:1338        Length:1338        Min.   :-27607.54   Min.   : 1122  
 Class :character   Class :character   1st Qu.: -1340.00   1st Qu.: 4740  
 Mode  :character   Mode  :character   Median :   -13.35   Median : 9382  
                                       Mean   :   136.09   Mean   :13270  
                                       3rd Qu.:  1427.87   3rd Qu.:16640  
                                       Max.   : 30313.76   Max.   :63770

Dplyr data explorations

Here I added a new column or variable called finalcosts where I added the the previous balance and the costs column together to make the finalcost column using mutate function.

# Load the dplyr package
library(dplyr)
# Convert the healthcare data.frame into a  tbl
healthcare1 <- as_tibble(healthcare)

# Display the healthcare tbl
head(healthcare)

# A tibble: 6 x 8
  age_yrs gender body_mass no_children smoker region    prev_balance  costs
    <dbl> <chr>      <dbl>       <dbl> <chr>  <chr>            <dbl>  <dbl>
1      18 female      42.2           0 yes    southeast      -17938. 38793.
2      43 female      30.7           2 no     northwest         195.  8311.
3      62 male        37.4           0 no     southwest       -4273. 12979.
4      49 female      23.2           2 no     northwest        1480. 10157.
5      46 male        40.4           2 no     northwest        -671.  8733.
6      63 male        36.8           0 no     northeast        5672. 13982.

# Create the object carriers
finalcosts <- healthcare1$costs
# Add the new variable prev_balance+costs to a copy of healthcare and save the result as g1.
g1 <- mutate(healthcare, finalcosts = costs + prev_balance)
glimpse(g1)

Observations: 1,338
Variables: 9
$ age_yrs      <dbl> 18, 43, 62, 49, 46, 63, 41, 55, 52, 25, 62, 48, 19,…
$ gender       <chr> "female", "female", "male", "female", "male", "male…
$ body_mass    <dbl> 42.240, 30.685, 37.400, 23.180, 40.375, 36.765, 33.…
$ no_children  <dbl> 0, 2, 0, 2, 2, 0, 3, 2, 0, 0, 0, 0, 1, 5, 2, 0, 1, …
$ smoker       <chr> "yes", "no", "no", "no", "no", "no", "no", "no", "n…
$ region       <chr> "southeast", "northwest", "southwest", "northwest",…
$ prev_balance <dbl> -17938.42104, 195.25679, -4272.92335, 1480.08209, -…
$ costs        <dbl> 38792.686, 8310.839, 12979.358, 10156.783, 8733.229…
$ finalcosts   <dbl> 20854.265, 8506.096, 8706.435, 11636.865, 8061.978,…

Body mass increase with final cost ( prev_balance + costs). I also factored in the graph to divide the smokers in blue and non smokers in red. Here you can see that non smokers are paying less for healthcare and smokers are paying a lot more around 25K-50K for healthcare cost. Insurance companies would have to charge smokers more in healthcare cost.

ggplot(data= g1, aes(x= body_mass, y = finalcosts, col=factor(smoker))) + geom_point() + geom_smooth(method = "lm", se = FALSE)

Here are the first 6 rows of the most significant variables in the healthcare dataset with the lowest p values in the data set. I listed the first 6 rows to exam the data set since printing all rows would take up too much space. Here you can see that a 63 yrs old person with a body mass index of 36.7 pays less healthcare cost compared to an 18 year old smoker with a body mass of 42. Just by looking at those two patients you can see that these variable are very significant to the cost of healthcare.

# Print out a tbl with the four columns of healthcare related to most signicant data 
mostsign<-select(healthcare, body_mass, age_yrs, smoker, no_children, costs)
head(mostsign)

# A tibble: 6 x 5
  body_mass age_yrs smoker no_children  costs
      <dbl>   <dbl> <chr>        <dbl>  <dbl>
1      42.2      18 yes              0 38793.
2      30.7      43 no               2  8311.
3      37.4      62 no               0 12979.
4      23.2      49 no               2 10157.
5      40.4      46 no               2  8733.
6      36.8      63 no               0 13982.

The arrange function arranges all the column from least to the most.

Lowest costs column shows non smoking males with medium body mass, linving in the southeast with no children have the least cost in healthcare.

People paying the most for healthcare costs are mostly smokers, people with negative prev_balances and are females with 4-3 or 0 children live in southwest, northeast, southeast.

arrangecosts<-arrange(healthcare, costs, body_mass, prev_balance, no_children)
arrangecosts

# A tibble: 1,338 x 8
   age_yrs gender body_mass no_children smoker region    prev_balance costs
     <dbl> <chr>      <dbl>       <dbl> <chr>  <chr>            <dbl> <dbl>
 1      18 male        23.2           0 no     southeast        -2.27 1122.
 2      18 male        30.1           0 no     southeast      -247.   1132.
 3      18 male        33.3           0 no     southeast       -19.9  1136.
 4      18 male        33.7           0 no     southeast       392.   1136.
 5      18 male        34.1           0 no     southeast       209.   1137.
 6      18 male        34.4           0 no     southeast        53.5  1137.
 7      18 male        37.3           0 no     southeast      -175.   1141.
 8      18 male        41.1           0 no     southeast       253.   1147.
 9      18 male        43.0           0 no     southeast      -419.   1149.
10      18 male        53.1           0 no     southeast       -22.1  1163.
# … with 1,328 more rows

# in arrange: lowest costs column shows males and no smokers with medium body mass, southeast with no children pay less healthcare cost

#people paying most healthcare costs are mostly smokers, have negative prev_balances and mostly females 4-3 or 0 children live in southwest, northeast, southeast

Linear Regression model for Healthcare dataset where test all variables against costs except for the previous balance varoable

mdl3 <- lm(costs ~. -prev_balance , data = healthcare)
summary(mdl3)


Call:
lm(formula = costs ~ . - prev_balance, data = healthcare)

Residuals:
     Min       1Q   Median       3Q      Max 
-11304.9  -2848.1   -982.1   1393.9  29992.8 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -11938.5      987.8 -12.086  < 2e-16 ***
age_yrs            256.9       11.9  21.587  < 2e-16 ***
gendermale        -131.3      332.9  -0.394 0.693348    
body_mass          339.2       28.6  11.860  < 2e-16 ***
no_children        475.5      137.8   3.451 0.000577 ***
smokeryes        23848.5      413.1  57.723  < 2e-16 ***
regionnorthwest   -353.0      476.3  -0.741 0.458769    
regionsoutheast  -1035.0      478.7  -2.162 0.030782 *  
regionsouthwest   -960.0      477.9  -2.009 0.044765 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6062 on 1329 degrees of freedom
Multiple R-squared:  0.7509,    Adjusted R-squared:  0.7494 
F-statistic: 500.8 on 8 and 1329 DF,  p-value: < 2.2e-16

1. Here is a linear regression model where we use all variables except previous balance.

Most significant variables are age_yr,body_mass,no children and smokers.
We want to know how well does the model fit the data.

We will use R2 for this.
R2 is the proportion of variability in Y that is explained by our model.
The R^2 is 0.75 which is good and adjusted r square(multiple features) is close to R^2.
We want a high R^2 value to show that our model is the best fit model.
R2 is always between 0 and 1
The bigger R2 is, the better your model fits the data
a small R2 doesn’t always mean the model is a poor fit
R2 always increases as you add more features to your model (the adjusted R2 should be used instead - it penalizes the R2 for each additional feature)

p-value in this case would be defined as: the probability of getting a coefficient as or more extreme than what we got, if the true coefficient was actually zero. We want a low p-Value (2.2e-16) which is a low pvalue(Pr is the symbol above for Pvalue)
Std. Error is the standard deviation of the sampling distribution of the estimate of the coefficient under the linear regression model assumptions. Since we did not normalize the coefficient we can not use the std. error from this summary. The Standard error is an estimate of the variance of the strength of the effect, or the strength of the relationship between each causal variable and the predicted variable. If it’s high, then the effect size will have to be stronger for us to be able to be sure that it’s a real effect, and not just an artefact of randomness.
t value is the value of the t-statistic for testing whether the corresponding regression coefficient is different from 0. The t-statistic is an estimate of how extreme the value you see is, relative to the standard error (assuming a normal distribution, centred on the null hypothesis).
Pr. is the p-value for the hypothesis test for which the t value is the test statistic. It tells you the probability of a test statistic at least as unusual as the one you obtained, if the null hypothesis were true. In this case, the null hypothesis is that the true coefficient is zero; if that probability is low, it’s suggesting that it would be rare to get a result as unusual as this if the coefficient were really zero.
The F statistic on the last line is telling you whether the regression as a whole is performing ‘better than random’ - any set of random predictors will have some relationship with the response, so it’s seeing whether your model fits better than you’d expect if all your predictors had no relationship with the response (beyond what would be explained by that randomness). This is used for a test of whether the model outperforms ‘noise’ as a predictor. The p-value in the last row is the p-value for that test, essentially comparing the full model you fitted with an intercept-only model.

Linear Regression on all the features or variables in the Healthcare data set

mdl <- lm(costs ~ ., data = healthcare)
summary(mdl)


Call:
lm(formula = costs ~ ., data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11671  -2862  -1018   1393  29499 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.187e+04  9.870e+02 -12.023  < 2e-16 ***
age_yrs          2.551e+02  1.191e+01  21.424  < 2e-16 ***
gendermale      -8.097e+01  3.333e+02  -0.243 0.808079    
body_mass        3.384e+02  2.856e+01  11.847  < 2e-16 ***
no_children      4.722e+02  1.376e+02   3.431 0.000619 ***
smokeryes        2.383e+04  4.127e+02  57.747  < 2e-16 ***
regionnorthwest -3.655e+02  4.756e+02  -0.769 0.442292    
regionsoutheast -1.030e+03  4.780e+02  -2.154 0.031410 *  
regionsouthwest -9.838e+02  4.774e+02  -2.061 0.039518 *  
prev_balance     7.932e-02  3.619e-02   2.192 0.028539 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6053 on 1328 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7501 
F-statistic:   447 on 9 and 1328 DF,  p-value: < 2.2e-16

Here is the summary of the linear regression with all the features. It looks like this r^2 and adjusted R^2 is higher than the one above but you also have to consider that more features giving you a higher R^2.
The p-value is the same and still significant. The adjusted R ^2 was higher in this model of all features compared to mdl3 above which had the prev_balance removed.

Box plot graphs of previous balance column vs costs

ggplot(data= healthcare, aes(X=cut(prev_balance, breaks = 15), y = costs)) + geom_boxplot()

# non linear graph that is evenly distributed

Looks like the pre_balance variable has a parabola with prices owed and owed to them spreading out from zero to the positive and negative evenly.

Scatter plot of age vs costs

ggplot(data= healthcare, aes(x= age_yrs, y = costs)) + geom_point() + geom_smooth(method = "lm", se = FALSE)

###This looks like there are colinearity with increase healthcare cost with increase in age.

Histogtam of the amount of patients at different age groups

ggplot(healthcare,aes(x=age_yrs)) + geom_histogram(bins=100,alpha=0.5,fill='blue')

###Here is a histogram of the number of peoples from 10-70 ages in the patient population. It look like there is an increase number of patients at age 10 years old. the rest of the histogram levels out.

Histogram of number of people at different BMI

ggplot(healthcare,aes(x=body_mass)) + geom_histogram(bins=100,alpha=0.5,fill='blue')

###This histogram shows a bell curve distribution of the patient population’s body mass index. The average body mass index is around 30 BMI. We have a few outlier patients with a BMI out in the 50 range and the minimum body mas is around 18 BMI. Otherwise the BMI has a normal distribution.

Histogram of the number of people paying different costs for healthcare in the dataset

ggplot(healthcare,aes(x=costs)) + geom_histogram(bins=100,alpha=0.5,fill='blue')

##Looks like most people are paying around less then 5,000 in healthcare cost. There are a few outliers that pay a lot more.

Histogram of the amount of people that carried a range of previous balance for healthcare.

ggplot(healthcare,aes(x=prev_balance)) + geom_histogram(bins=100,alpha=0.5,fill='blue')

##This is very similar to boxplot done earlier showing a normal distribution.

Histogram of number of patients with 0-5 children in thier family.

ggplot(healthcare,aes(x=no_children)) + geom_histogram(bins=20,alpha=0.5,fill='blue')

###Looks like there are more people paying for health care in this data set who have no children or between 0-2 kids in this data set. Maybe more people are single not married yet.

Boxplot of patients from different regions vs the costs of healthcare

ggplot(healthcare) + geom_boxplot(aes(x= factor(region), y =costs))

#region is similar except the southeast show that the cost of healthcare is higher.

Looks like we have people in southeast paying more for healthcare. The other regions look very close to each other with southwest a little lower in healthcare cost.

Scatter plot showing healthcare cost increases with BMI, vs regions vs gender

ggplot(data= healthcare, aes(x= body_mass, y = costs, color = factor(gender))) + geom_point(aes(shape=factor(region))) + geom_smooth(method = "lm", se = FALSE)

#more body mass means your costs goes us as the bodymass increase

Healthcare cost increases with body masss. The male blue line shows that males under twenty pay less for healthcare and after age 23 they start paying the same as females for healthcare. But when males reach their 30’s they start paying more for healthcare cost compated to females. This scatter graph it is difficult to determine where people live determines the healthcare cost.

ggplot(data= healthcare, aes(x= no_children, y = costs, color = factor(gender))) + geom_point(aes(shape=factor(region)), size=2) + geom_smooth(method = "lm", se = FALSE)

#it is possible people large children incure less cost but htis is not strong.

looks like male and female both increase their healthcare cost as they have children. It seems like males pay a litte more if they grow their family. The region location of patiensts is hard to read in this graph. But seem like more southeast outliers paying 40K-60K

Scatter plot of BMI vs gender and region

ggplot(data= healthcare, aes(x= age_yrs, y = costs, color=factor(gender)) )+ geom_point(aes(shape=factor(region))) + geom_smooth(method = "lm", se = FALSE)

###There is a correlation with age increaseing with cost and males pay more than females at the parallel rate.

Scatterplot heat map

pl <-ggplot(healthcare,aes(x=body_mass, y=costs))
pl2 <- pl+ geom_point(aes(color=no_children),size=2)
pl3 <- pl2 + scale_color_gradient(low='blue',high='red')
print(pl3)

###1.It looks like body mass increase as people pay more. 2.It seems hard to tell about how the number of children effect cost.
3.It seems like the blue=0 children are the ones at the bottom of the graph indicating people with zero children pay less cost for healthcare.

ggplot(data= healthcare, aes(x= prev_balance, y = costs,  color = factor(gender))) + geom_point()

#doesn't look like there is a correlation

Doesn’t look like there is a correlation. Most people do seem to have a previous balance of zero.

ggplot(data= healthcare, aes(x= body_mass, y = costs,  color = factor(gender))) + geom_point() + geom_smooth(method = "lm", se = FALSE)

health_sum =  summary(mdl)
health_sum


Call:
lm(formula = costs ~ ., data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11671  -2862  -1018   1393  29499 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.187e+04  9.870e+02 -12.023  < 2e-16 ***
age_yrs          2.551e+02  1.191e+01  21.424  < 2e-16 ***
gendermale      -8.097e+01  3.333e+02  -0.243 0.808079    
body_mass        3.384e+02  2.856e+01  11.847  < 2e-16 ***
no_children      4.722e+02  1.376e+02   3.431 0.000619 ***
smokeryes        2.383e+04  4.127e+02  57.747  < 2e-16 ***
regionnorthwest -3.655e+02  4.756e+02  -0.769 0.442292    
regionsoutheast -1.030e+03  4.780e+02  -2.154 0.031410 *  
regionsouthwest -9.838e+02  4.774e+02  -2.061 0.039518 *  
prev_balance     7.932e-02  3.619e-02   2.192 0.028539 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6053 on 1328 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7501 
F-statistic:   447 on 9 and 1328 DF,  p-value: < 2.2e-16

The male blue line shows that males under twenty pay less for healthcare and after age 23 they start paying the same as females for healthcare. But when males reach their 30’s they start paying more for healthcare cost compated to females.

ggplot(data= healthcare, aes(x= age_yrs, y = costs,  color = factor(gender))) + geom_point() + geom_smooth(method = "lm", se = FALSE)

health_sum =  summary(mdl)
health_sum


Call:
lm(formula = costs ~ ., data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11671  -2862  -1018   1393  29499 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.187e+04  9.870e+02 -12.023  < 2e-16 ***
age_yrs          2.551e+02  1.191e+01  21.424  < 2e-16 ***
gendermale      -8.097e+01  3.333e+02  -0.243 0.808079    
body_mass        3.384e+02  2.856e+01  11.847  < 2e-16 ***
no_children      4.722e+02  1.376e+02   3.431 0.000619 ***
smokeryes        2.383e+04  4.127e+02  57.747  < 2e-16 ***
regionnorthwest -3.655e+02  4.756e+02  -0.769 0.442292    
regionsoutheast -1.030e+03  4.780e+02  -2.154 0.031410 *  
regionsouthwest -9.838e+02  4.774e+02  -2.061 0.039518 *  
prev_balance     7.932e-02  3.619e-02   2.192 0.028539 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6053 on 1328 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7501 
F-statistic:   447 on 9 and 1328 DF,  p-value: < 2.2e-16

Another similar graph with coloring the gender. There seems to be not much differene between male and female.

Linear Regression on all the features or variables in the Healthcare data set

health_sum =  summary(mdl)
health_sum


Call:
lm(formula = costs ~ ., data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11671  -2862  -1018   1393  29499 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.187e+04  9.870e+02 -12.023  < 2e-16 ***
age_yrs          2.551e+02  1.191e+01  21.424  < 2e-16 ***
gendermale      -8.097e+01  3.333e+02  -0.243 0.808079    
body_mass        3.384e+02  2.856e+01  11.847  < 2e-16 ***
no_children      4.722e+02  1.376e+02   3.431 0.000619 ***
smokeryes        2.383e+04  4.127e+02  57.747  < 2e-16 ***
regionnorthwest -3.655e+02  4.756e+02  -0.769 0.442292    
regionsoutheast -1.030e+03  4.780e+02  -2.154 0.031410 *  
regionsouthwest -9.838e+02  4.774e+02  -2.061 0.039518 *  
prev_balance     7.932e-02  3.619e-02   2.192 0.028539 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6053 on 1328 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7501 
F-statistic:   447 on 9 and 1328 DF,  p-value: < 2.2e-16

This model with cost and body mass is more correlated with R^2 0.75 and pvalue = 2.2e-16

Linear Regression on all the features or variables except gender in the Healthcare data set

# bodymass model
modelpract <- lm(costs ~ . -gender, healthcare )

summary(modelpract)


Call:
lm(formula = costs ~ . - gender, data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11713  -2822  -1009   1415  29460 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.190e+04  9.782e+02 -12.162  < 2e-16 ***
age_yrs          2.552e+02  1.190e+01  21.441  < 2e-16 ***
body_mass        3.380e+02  2.852e+01  11.853  < 2e-16 ***
no_children      4.716e+02  1.375e+02   3.429 0.000625 ***
smokeryes        2.382e+04  4.113e+02  57.918  < 2e-16 ***
regionnorthwest -3.652e+02  4.755e+02  -0.768 0.442607    
regionsoutheast -1.029e+03  4.778e+02  -2.154 0.031422 *  
regionsouthwest -9.835e+02  4.772e+02  -2.061 0.039495 *  
prev_balance     7.993e-02  3.609e-02   2.215 0.026930 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6051 on 1329 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7503 
F-statistic: 503.2 on 8 and 1329 DF,  p-value: < 2.2e-16

coef(modelpract)

    (Intercept)         age_yrs       body_mass     no_children 
  -1.189732e+04    2.551808e+02    3.380214e+02    4.715901e+02 
      smokeryes regionnorthwest regionsoutheast regionsouthwest 
   2.382201e+04   -3.651658e+02   -1.029253e+03   -9.835277e+02 
   prev_balance 
   7.993046e-02

This linear regression model is similar to the above model with the same p value and R^2 value

Linear Regression the features of body mass in the Healthcare data set vs costs.

# bodymass model
mod <- lm(costs ~ body_mass, data = healthcare )
summary(mod)


Call:
lm(formula = costs ~ body_mass, data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-20956  -8118  -3757   4722  49442 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1192.94    1664.80   0.717    0.474    
body_mass     393.87      53.25   7.397 2.46e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 11870 on 1336 degrees of freedom
Multiple R-squared:  0.03934,   Adjusted R-squared:  0.03862 
F-statistic: 54.71 on 1 and 1336 DF,  p-value: 2.459e-13

coef(mod)

(Intercept)   body_mass 
   1192.937     393.873

Mean Residuals for the Linear regression ran above.

Mod

mean(residuals(mod))

[1] 3.247255e-13

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e)

Each data point has one residual. Residual = Observed value - Predicted value. e = y - ŷ Both the sum and the mean of the residuals are equal to zero.

Modelpract

mean(residuals(modelpract))

[1] -3.604531e-13

MDL

mean(residuals(mdl))

[1] 8.068417e-14

All the Mean Residuals were equal to zero. Meaning that the Residual = Observed value - Predicted value. This says that observed value and predicted values were very close they cancel each other out.

RMSE Root Mean Square Error

sqrt(sum(residuals(mod)^2)/df.residual(mod))

[1] 11873.86

Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells you how concentrated the data is around the line of best fit.

sqrt(sum(residuals(mdl)^2)/df.residual(mdl))

[1] 6053.441

Both the RMSE look very high.

When the RMSE is spread out and data has higher rmse we have a poor model fit prediction Lower rmse closer strong fitted and acual value.

sqrt(sum(residuals(modelpract)^2)/df.residual(modelpract))

[1] 6051.298

The RMSE data seems to say taht Maybe using Linear regression on the data set is not the best model to predict the cost of healthcare.

Here we will split our Healthcare dataset in to a Training and Testing set to test out our Linear regression model and see if we can train our model and test it to see how accuarte it can predict the cost of healthcare.

Spliting Data into train and test set with caTools

library(caTools)
#set ad seed
set.seed(101)
#split up samples
sample<- sample.split(healthcare$costs, SplitRatio = 0.7)
#70% of data ->train
train<- subset(healthcare,sample == TRUE)
#30% will be test
test <- subset(healthcare, sample == FALSE)

#model of building linear regression model in R and train
healthmodel <- lm(costs~., train) # all features

healthmodel2 <- lm(costs ~ .-prev_balance -gender -region, train )

print(summary(healthmodel))


Call:
lm(formula = costs ~ ., data = train)

Residuals:
     Min       1Q   Median       3Q      Max 
-11416.1  -2930.5   -945.5   1726.7  29501.6 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.209e+04  1.161e+03 -10.412   <2e-16 ***
age_yrs          2.555e+02  1.429e+01  17.878   <2e-16 ***
gendermale      -3.309e+02  4.002e+02  -0.827   0.4086    
body_mass        3.541e+02  3.406e+01  10.395   <2e-16 ***
no_children      4.335e+02  1.673e+02   2.592   0.0097 ** 
smokeryes        2.395e+04  4.908e+02  48.803   <2e-16 ***
regionnorthwest -5.379e+02  5.782e+02  -0.930   0.3524    
regionsoutheast -1.002e+03  5.816e+02  -1.723   0.0853 .  
regionsouthwest -1.222e+03  5.700e+02  -2.144   0.0323 *  
prev_balance     5.198e-02  4.160e-02   1.249   0.2118    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6079 on 926 degrees of freedom
Multiple R-squared:  0.7603,    Adjusted R-squared:  0.758 
F-statistic: 326.4 on 9 and 926 DF,  p-value: < 2.2e-16

print(summary(healthmodel2))


Call:
lm(formula = costs ~ . - prev_balance - gender - region, data = train)

Residuals:
   Min     1Q Median     3Q    Max 
-11932  -2903   -865   1625  29288 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -12570.02    1106.27 -11.362   <2e-16 ***
age_yrs        257.87      14.25  18.093   <2e-16 ***
body_mass      338.76      32.41  10.454   <2e-16 ***
no_children    420.24     167.02   2.516    0.012 *  
smokeryes    23985.57     487.42  49.209   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6087 on 931 degrees of freedom
Multiple R-squared:  0.7584,    Adjusted R-squared:  0.7573 
F-statistic: 730.5 on 4 and 931 DF,  p-value: < 2.2e-16

Here we set a seed so the training set and test set can be reproducible. Otherwise it would be random and we can’t reproduce the data for practice.

In a non practice enviromnent you would not set the seed for training/test set.

Residual plot to determine the random noise of the model

library(ggplot2)
library(broom)
#graph a model for residual test
res_model <- lm(costs ~ ., healthcare)
#get observ level info
model_observe <- augment(res_model)
#see the result
model_observe

# A tibble: 1,338 x 15
    costs age_yrs gender body_mass no_children smoker region prev_balance
    <dbl>   <dbl> <chr>      <dbl>       <dbl> <chr>  <chr>         <dbl>
 1 38793.      18 female      42.2           0 yes    south…      -17938.
 2  8311.      43 female      30.7           2 no     north…         195.
 3 12979.      62 male        37.4           0 no     south…       -4273.
 4 10157.      49 female      23.2           2 no     north…        1480.
 5  8733.      46 male        40.4           2 no     north…        -671.
 6 13982.      63 male        36.8           0 no     north…        5672.
 7  8538.      41 female      33.2           3 no     north…        -654.
 8 12269.      55 female      32.8           2 no     north…       -2324.
 9  9635.      52 female      37.4           0 no     south…        1238.
10  2138.      25 male        25.7           0 no     south…         522.
# … with 1,328 more rows, and 7 more variables: .fitted <dbl>,
#   .se.fit <dbl>, .resid <dbl>, .hat <dbl>, .sigma <dbl>, .cooksd <dbl>,
#   .std.resid <dbl>

#using model_observe draw scatter plot of residual vs fitted values
ggplot(model_observe, aes(x=.fitted, y=.resid))+
  geom_point()

###Looks like the residuals are not distribued randomly. There is some weird pattern and the correlation not accounted for . So this might be a bad example of a residual distribution. Maybe linear regression is not the best model for this data set to predict the cost of healthcare.

library(ggplot2)
library(broom)
#graph a model for residual test
#res_model <- augment(lm(costs ~ ., healthcare ))
#get observ level info
#model_observe <- augment(res_model)
#see the result
model_observe

# A tibble: 1,338 x 15
    costs age_yrs gender body_mass no_children smoker region prev_balance
    <dbl>   <dbl> <chr>      <dbl>       <dbl> <chr>  <chr>         <dbl>
 1 38793.      18 female      42.2           0 yes    south…      -17938.
 2  8311.      43 female      30.7           2 no     north…         195.
 3 12979.      62 male        37.4           0 no     south…       -4273.
 4 10157.      49 female      23.2           2 no     north…        1480.
 5  8733.      46 male        40.4           2 no     north…        -671.
 6 13982.      63 male        36.8           0 no     north…        5672.
 7  8538.      41 female      33.2           3 no     north…        -654.
 8 12269.      55 female      32.8           2 no     north…       -2324.
 9  9635.      52 female      37.4           0 no     south…        1238.
10  2138.      25 male        25.7           0 no     south…         522.
# … with 1,328 more rows, and 7 more variables: .fitted <dbl>,
#   .se.fit <dbl>, .resid <dbl>, .hat <dbl>, .sigma <dbl>, .cooksd <dbl>,
#   .std.resid <dbl>

#using model_observe draw scatter plot of residual vs fitted values
ggplot(model_observe, aes(x=.fitted, y=.resid))+
  geom_point()+ geom_hline(yintercept = 0)

Looks like the residuals are not distribued normally. There is some weird pattern and the correlation not accounted for. So this might be bad example of residual distribution. Maybe linear regression is not the best model for this data set to predict the cost of healthcare. ( there was an issue with running this augment and I commented it out)

Scatterplot looking at the BMI vs Cost and filtering the outliers with body mass greater than 35

library(tidyverse)
# This plot is shown
p <- ggplot(healthcare, aes(x = body_mass, y = costs)) + 
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) 

# Filter to remove the outlier
healthcareoutlier <- healthcare %>% 
  filter( body_mass < 30)

p +
  # Add another smooth lin .reg. layer, no ribbon, 
  # hypdata_no_outlier data, colored red
  geom_smooth(
    method = "lm", se = FALSE, 
    data = healthcareoutlier, color = "red"
  )

The red line shows the linear regression line that is filters out the BMI greater than 30. You can see the slope is still slightly tilted compared to the original line blue line.People who have a BMI under 30 increase in healthcare cost slower compared to before we filtered the outliers out of the equation. This is not alway the best practice. Here we can play around with filtering outlier out of the linear regression model.

#how many rows are in the data
n <- nrow(healthcare)
n

[1] 1338

#rows
nrow(healthcare)

[1] 1338

#calculate 80% of the rows
n_train <- round(0.80 * n)
n_train

[1] 1070

set.seed(123)
#create an index that is 80% of the data
train_ind <- sample(1:n, n_train)

#seperate the trian protion 
health_train <- healthcare[train_ind,]

#see if it worked but counting 

#using the "-" sign seperate the test portion 
health_test <-  healthcare[-train_ind,]

nrow(health_test)

[1] 268

#add them together to see if it worked 
nrow(health_test) + nrow(health_train)

[1] 1338

confirmed the test train split worked

costs.predictions <- predict(mdl, health_train)
results  <- c(costs.predictions, health_test$costs)
results

          1           2           3           4           5           6 
 7857.80654 25155.68215 12265.70836  7175.19469  4176.87015  8634.95989 
          7           8           9          10          11          12 
 9915.09663 33727.54665  6194.82018 12158.22323  3605.16115 12877.22841 
         13          14          15          16          17          18 
 5487.32024  6366.70236 31000.56838 16611.12040 33924.23979 13542.37650 
         19          20          21          22          23          24 
28592.21594  3516.36839 -1144.96971 34498.62113 33629.79539 29790.84729 
         25          26          27          28          29          30 
10047.40619  5435.19171 11712.74324  6947.76261 12249.08239  6053.50888 
         31          32          33          34          35          36 
35596.88092  4007.25585  4605.70660 34230.32059 31220.31122 33633.17190 
         37          38          39          40          41          42 
30212.14297 10305.26780 11817.28848 35799.24565  4776.90488  3881.51717 
         43          44          45          46          47          48 
26218.58256  7923.20448 10883.08986  5458.49431  5347.22878 26426.79788 
         49          50          51          52          53          54 
 8668.73697  7844.45408 10640.64153 10858.94829 41292.71162  5957.16891 
         55          56          57          58          59          60 
 1877.68390  3914.29906 13897.32009 31100.97726 22860.84127 15754.77359 
         61          62          63          64          65          66 
14012.92494  5546.92518  8121.50719  8949.21261 14019.10917  9630.26910 
         67          68          69          70          71          72 
17098.33083 13774.94004  8618.89831 28502.74877  3684.80106 39005.45721 
         73          74          75          76          77          78 
10518.82957 28395.07743 12497.04194  1988.95906  5606.05544  4456.10104 
         79          80          81          82          83          84 
39310.64496  6661.23822  2837.80891  1899.55359 31560.65859  5382.13551 
         85          86          87          88          89          90 
29258.31369  8210.81214 13655.34178 13249.60818 15168.95500 12236.21210 
         91          92          93          94          95          96 
38668.17832 28282.96715  5443.89880  3035.44714  7147.58833 13044.12250 
         97          98          99         100         101         102 
 9696.00811  9003.54269  1814.70665 15051.95970 10215.78199 35589.85974 
        103         104         105         106         107         108 
10441.15156 32124.10086 11695.92888  2403.09129  4497.29261 10653.78036 
        109         110         111         112         113         114 
33979.85781  8005.23456 11167.54145 14627.05343 17195.83092 10514.61670 
        115         116         117         118         119         120 
35240.11073  4331.98518 11412.36877  8765.86907  3118.30871  8570.62576 
        121         122         123         124         125         126 
13227.27116 12165.59463  3395.22574  6355.89205 11076.94912 14782.64083 
        127         128         129         130         131         132 
 1993.81470  4393.84703 12394.48738    74.09649  9697.64273 37082.32562 
        133         134         135         136         137         138 
14434.45783 36107.07037 14935.60653 30831.83248 11703.46089 10282.47315 
        139         140         141         142         143         144 
12004.40482 16768.66340 14444.80815  6263.69901  6566.19998  7810.77861 
        145         146         147         148         149         150 
 8654.89551  2199.29081 34879.63399  2551.73831  3705.27558  3412.36002 
        151         152         153         154         155         156 
15928.63967 12522.78642   404.29404 12532.22105  2724.72219  5519.80667 
        157         158         159         160         161         162 
37167.64018 13038.44078   927.38904  8516.75395 11437.30736  9050.99741 
        163         164         165         166         167         168 
11552.04579 12863.00133 11837.27624 17091.71655  9480.10276  2758.33798 
        169         170         171         172         173         174 
11931.91041 13802.06920  9414.08585  9595.14149 10483.73897   224.05557 
        175         176         177         178         179         180 
 9899.38842  4084.97619 12849.23709 10575.71981  5402.58355 30846.45887 
        181         182         183         184         185         186 
17005.46352 11680.69738 13232.49764 11011.72499  4780.56017 38140.39914 
        187         188         189         190         191         192 
 8964.05500  9708.87057 24280.41545 32742.51065 14546.18490  7924.79694 
        193         194         195         196         197         198 
32825.66912  8435.40721 11098.01726 14983.35327 38452.87173  5488.11617 
        199         200         201         202         203         204 
26073.54193   184.15839  8829.70722  8676.58285  7565.80309 27209.40163 
        205         206         207         208         209         210 
33152.60180  3679.58658  2891.10808  8806.61191 13850.31901  7062.82644 
        211         212         213         214         215         216 
15684.04085 13278.76559 11213.73175  4285.01088 13392.11370 31123.71560 
        217         218         219         220         221         222 
 4449.33707  4022.10702  5302.02769 28627.41497 13361.52660 27165.01534 
        223         224         225         226         227         228 
 7257.54822 28298.23576 32375.82662 33488.57371 13053.15533 14770.63770 
        229         230         231         232         233         234 
29302.02886 17304.84782  -101.77548  7678.26114 32162.50933  8877.97854 
        235         236         237         238         239         240 
 7764.66227  2505.83761  9757.07814  1825.00469  1206.60628 15901.91207 
        241         242         243         244         245         246 
10296.50918 28727.28290  5881.48497   436.88431 32440.77471  3107.04258 
        247         248         249         250         251         252 
28305.93121  4269.48934 15148.43300 34722.62545  9841.91887 23262.74619 
        253         254         255         256         257         258 
 6306.33614 31015.88824  5475.35874  8328.09462  8320.06349  4270.66563 
        259         260         261         262         263         264 
 8086.72607  -166.85565 11679.72401 11156.71358 11313.97280  9759.32276 
        265         266         267         268         269         270 
14781.46994 11174.49016  7131.10737  4905.21709 14413.77285  8658.45509 
        271         272         273         274         275         276 
16597.91633 11176.62922  5045.16268 12421.42107 28498.26359  1097.62995 
        277         278         279         280         281         282 
11883.57391  3722.37700  8642.82379 10190.31942  9127.33622  9400.35121 
        283         284         285         286         287         288 
 5443.92906  9355.50352  1064.90876  7912.41776 33707.97653  3404.60716 
        289         290         291         292         293         294 
 9151.77927  8126.91481 12300.76206 12281.68805 13580.55689 10249.99316 
        295         296         297         298         299         300 
 5270.35712  6111.35399 33782.24128  1381.89116  4426.52106 16971.22641 
        301         302         303         304         305         306 
15484.64007  2151.83646  7447.59701 28214.58403 26967.13474  9753.47444 
        307         308         309         310         311         312 
30321.84921 13169.01220  2924.32209  -954.39433   844.09630  6938.34743 
        313         314         315         316         317         318 
 7751.01386  5348.19253 38163.09742  7865.98600  2178.33652  2616.89145 
        319         320         321         322         323         324 
 6825.07171  4130.58668  5555.26356 10381.37631 29396.33879 10358.88588 
        325         326         327         328         329         330 
 2252.75092 37292.98553  2339.42270  7676.79306  2587.72805 33093.88582 
        331         332         333         334         335         336 
 4745.88738   191.38740  5434.04172  4780.80227  7461.37543  6126.25619 
        337         338         339         340         341         342 
 5681.05925  1115.60736 12995.61501  4649.91272  8794.95858 36809.00957 
        343         344         345         346         347         348 
15924.96688  7914.91107  5710.07339  2182.21958 24999.45883 32779.37793 
        349         350         351         352         353         354 
 1793.74867 37277.76922 10551.48989  5743.36514  5436.82675  8207.25964 
        355         356         357         358         359         360 
14770.06944 15128.83331 11256.28914 25906.15932  7141.20801 14088.78981 
        361         362         363         364         365         366 
 7973.58880 29638.13093  6915.07264  6401.45187  8225.66089  8214.01927 
        367         368         369         370         371         372 
 5290.95429  9689.88868  5765.17699  4118.78788  7804.80096 11147.16260 
        373         374         375         376         377         378 
10451.94209 14878.27668 11595.39007 15854.18154 39186.06403 35434.36981 
        379         380         381         382         383         384 
27809.52253  8650.31258  1227.13993 34569.08874  8227.41828  8878.75673 
        385         386         387         388         389         390 
11118.56011  9166.20634 39139.16266  8867.18056  9111.25588 35167.54113 
        391         392         393         394         395         396 
 2210.31621 12712.40436  1948.93310 14134.19575 39520.25875 11082.67597 
        397         398         399         400         401         402 
28221.55336  6379.90715 11335.25383 32472.56986  5673.91491 35622.68069 
        403         404         405         406         407         408 
12639.90735  5509.07809 36026.96181  9590.30907 11006.81328 33904.13291 
        409         410         411         412         413         414 
 7054.07621  5063.98434 12674.62595  9617.58903  3159.16572  1573.89523 
        415         416         417         418         419         420 
36388.07266  6471.23204 12712.95151 10682.13881 12002.41255 34261.26004 
        421         422         423         424         425         426 
10607.37464  6828.88181  7008.79800 13149.00177 11843.23667 11614.10251 
        427         428         429         430         431         432 
12665.18604  8022.18336  9636.85979  6360.13996 11438.33927  8455.51519 
        433         434         435         436         437         438 
15194.02863 12882.65975  9463.65142  2209.44851 33547.13541 15284.57599 
        439         440         441         442         443         444 
 3588.82084 31666.75247 11001.18695 32474.49128 13711.03684 11018.24286 
        445         446         447         448         449         450 
15515.02918  6565.37207 28756.19281 11316.48414  6303.43175 14910.55715 
        451         452         453         454         455         456 
 8850.30600  8617.88523  1857.96411  6627.57960  4191.01229 11924.16269 
        457         458         459         460         461         462 
 7282.30445 10406.65734  9991.77953 12913.81193  8883.72084  5744.44886 
        463         464         465         466         467         468 
 9776.39419  3736.56767  8259.53047  3413.93660 28057.08643 31312.76783 
        469         470         471         472         473         474 
 5076.95822 27250.48512 10622.75419  9823.61867  3663.61912 36186.37634 
        475         476         477         478         479         480 
 9156.87314  5367.71614 27704.76615  7645.98384   307.40985 26164.23885 
        481         482         483         484         485         486 
11388.24449  3638.08622 30788.98873  7295.42793  2467.72507 12775.09082 
        487         488         489         490         491         492 
11427.54522  8858.33488  7964.10289 14981.52553 14872.77080 30912.33886 
        493         494         495         496         497         498 
12625.47824  5783.66398  3677.76594 12429.54490 15609.01452 13170.55061 
        499         500         501         502         503         504 
28826.41100  3001.42312 14671.80529 29351.78518  8254.87771 12901.37703 
        505         506         507         508         509         510 
10457.07148 11019.98520 26333.79115  5689.45842  7057.76177 10257.63823 
        511         512         513         514         515         516 
 5071.31229  8931.75321 11891.31010 10902.24349  6926.11555 15400.29578 
        517         518         519         520         521         522 
13117.99524 13802.25510  3957.06771 26767.25283 12313.19186  6165.69363 
        523         524         525         526         527         528 
35056.31410  3269.11662  6780.72517 32670.05982 12648.94457 14422.16561 
        529         530         531         532         533         534 
11817.87231 12684.59358 10671.61872  5032.12749 11801.48506 29982.70096 
        535         536         537         538         539         540 
 3992.61159  4484.20876 32026.00151  4941.64241   398.39453  2160.22330 
        541         542         543         544         545         546 
12336.56525 10622.69023   422.81563  4436.00134  6391.96962  4708.43141 
        547         548         549         550         551         552 
38014.02817 12097.61595  8235.01167 10906.29262 10517.86336 10666.15213 
        553         554         555         556         557         558 
39703.80991  9872.81848  6720.74802 11093.44107 31431.58677  6859.97047 
        559         560         561         562         563         564 
16859.92972  3444.13308 13243.09823 14763.88253   -87.93788 32162.25850 
        565         566         567         568         569         570 
 7583.86127 30981.95430  2081.43771 12385.29644  7213.32570 27435.03768 
        571         572         573         574         575         576 
 8076.80743  1636.95749 11237.19710 35839.26513  8974.94066  4598.05605 
        577         578         579         580         581         582 
32431.68445  9643.34519  9316.63225 12807.52463  1771.77509 39305.16479 
        583         584         585         586         587         588 
-1090.50965 15475.25669  9191.65325 14850.33577  3176.09933  6633.12079 
        589         590         591         592         593         594 
 7604.07178  5382.70642 11875.69657  3071.27162 16239.31778 26957.17857 
        595         596         597         598         599         600 
 6948.47079 11732.37966  7388.10228  5682.43873 10540.82229  9867.56956 
        601         602         603         604         605         606 
  -31.36893 29002.72766 31026.53879 39292.26192 36741.75288  7514.93206 
        607         608         609         610         611         612 
12254.66976  6351.00200 34851.78300 12893.37033 41834.90820 24792.22351 
        613         614         615         616         617         618 
 5295.87938  5122.86176  4629.59002  9516.13787 15043.84276 29271.40399 
        619         620         621         622         623         624 
16446.52762  5569.93502 27550.79420 11369.23568 11748.90176 10507.24503 
        625         626         627         628         629         630 
 9094.04067 10527.75455  3210.71225 10465.11232  7258.27036 12406.98713 
        631         632         633         634         635         636 
15811.62527 39487.17229 25905.12622 -1742.70804 12524.21045 39426.24248 
        637         638         639         640         641         642 
 3794.33654 39203.41728  6177.65736 12933.75011  4231.17392  7803.97579 
        643         644         645         646         647         648 
12160.32758  8505.44435  1588.15587  1475.54635 32952.73801 14089.25676 
        649         650         651         652         653         654 
 3316.34152  3906.87356 36582.53122 27917.38875 11871.64275  7154.07259 
        655         656         657         658         659         660 
-1516.76134  2800.30097  1924.19368 14201.10516  9554.74680  5649.10423 
        661         662         663         664         665         666 
 6051.58680  1968.20325  5041.52920 14942.74106 16532.35830  4233.17261 
        667         668         669         670         671         672 
12464.25922  3007.51799  7345.24166  9636.39584 37660.87231 32827.38100 
        673         674         675         676         677         678 
 4590.32391  8735.92742 35236.20128  4886.72542 25444.93793  9391.72352 
        679         680         681         682         683         684 
16842.25399 15234.75786  9218.83687  8434.72436  3420.45893  3133.24842 
        685         686         687         688         689         690 
 9885.89890 13000.77025  2032.42925  6887.24469 10180.08710  6529.18072 
        691         692         693         694         695         696 
 2916.91787 35906.63639  6124.23520 12976.49639  8732.69842 30556.13050 
        697         698         699         700         701         702 
10502.36220  4155.58543  6746.99586  3262.36163  9098.89416  6854.45079 
        703         704         705         706         707         708 
14757.77104 10832.71911 26463.58119 12020.85918  4037.70047 26806.20389 
        709         710         711         712         713         714 
 7928.81790   972.66648 12792.99980 16738.24276 31273.55114 13756.27302 
        715         716         717         718         719         720 
 6450.13552 25315.49973 13975.08197 15202.14730  4201.12832 12048.46432 
        721         722         723         724         725         726 
11359.91033 23778.97457  -495.82041 12086.86441  6379.04550  7455.72374 
        727         728         729         730         731         732 
28838.25009 35715.45468  3994.34870  3137.61270 34710.01850  9073.55886 
        733         734         735         736         737         738 
14441.21579 31434.57032 10908.10316 10420.79147 11884.63234 32722.01192 
        739         740         741         742         743         744 
 8012.60254  9588.73036 23596.69884 14916.65191 36082.55096 14993.81589 
        745         746         747         748         749         750 
 3169.77051  1924.10671 11009.55709 39833.42504 11115.00009 12435.21415 
        751         752         753         754         755         756 
12691.64223  4694.06037 13433.93344  6467.60716  3511.22443 12793.50008 
        757         758         759         760         761         762 
 2827.43602 12738.58212 11567.06756  1183.32832 11299.29012 12617.08515 
        763         764         765         766         767         768 
 1386.37613  -654.57994  6839.07480  9096.85628 26750.23997 14660.56831 
        769         770         771         772         773         774 
18900.80948 33170.31156  8680.10685  7630.15687  8319.60544  6240.17072 
        775         776         777         778         779         780 
23699.65414 26980.41606 37613.16950 16271.81359 12129.29528 38777.21056 
        781         782         783         784         785         786 
 6381.11839 14903.88882 23351.81431 -1999.60719  2762.48329 10672.58990 
        787         788         789         790         791         792 
27442.70701 15537.97540  6621.60056  8612.19781  3221.82452  8694.40616 
        793         794         795         796         797         798 
10573.21005 29596.03757 38183.44498  3929.98625 13159.88478 11183.36311 
        799         800         801         802         803         804 
30524.45547 15946.91442  4414.30784 13556.44458 12482.82931 17421.44893 
        805         806         807         808         809         810 
 9506.70854  3497.90545 27456.00704 14742.68980 12516.12169  2304.87151 
        811         812         813         814         815         816 
14374.84931  8039.30911   875.00071  6585.96987 27175.15336  9686.75466 
        817         818         819         820         821         822 
 7052.64470  7106.11046  4095.59983  7677.40355 32836.99546  3070.91839 
        823         824         825         826         827         828 
27839.42116 25599.82592 13519.25209  4597.45705  6721.72971  4218.69047 
        829         830         831         832         833         834 
   78.50513  7122.25134  7695.44047  9212.73653   356.74150 42101.38465 
        835         836         837         838         839         840 
 6231.72543  7112.27959  6425.67539 10093.08481 12163.56105 11562.66242 
        841         842         843         844         845         846 
35111.28729 39572.46929 39865.30103  7596.07317 39495.58279  4143.94324 
        847         848         849         850         851         852 
 -553.23712 14649.21250 14057.83940 34731.18822 10279.89853 26733.44538 
        853         854         855         856         857         858 
 5880.02298  3997.20751  5190.89267  8422.65267 11576.03841 13498.00573 
        859         860         861         862         863         864 
35026.43788 27624.51327  5590.14044 11415.08494 35700.34633  7139.92403 
        865         866         867         868         869         870 
  712.80331 11539.60253  5765.70888 13052.04921 40381.57307  8716.45651 
        871         872         873         874         875         876 
10194.31847  9253.04684 12097.11798 11676.02050  7377.83956 15533.47671 
        877         878         879         880         881         882 
29803.77328 11680.39066  2765.40981  2192.22349   200.79232 15142.64260 
        883         884         885         886         887         888 
 6145.25763  3799.15262 29961.95187  9339.47627  3253.92547 13954.20126 
        889         890         891         892         893         894 
10293.27138  2225.70446 14460.26272 15160.01978  8039.68617  8568.27675 
        895         896         897         898         899         900 
 2943.52057  9594.29476 12966.63513 11746.11391  6136.35865  9348.04237 
        901         902         903         904         905         906 
 8918.07425 33177.56275  2980.88092 10484.62575  2060.54424  9271.45364 
        907         908         909         910         911         912 
 4934.28926  1889.79621 27950.49137 15036.84594 10080.78333 14555.31224 
        913         914         915         916         917         918 
13781.48672 10357.30975 12137.88768  5756.88612  2186.28782 11077.44652 
        919         920         921         922         923         924 
31900.12722 38030.74958  9157.18297 10324.76267 12295.44522 35802.48251 
        925         926         927         928         929         930 
27520.39594  5077.70873  1763.83035 37823.84266  9252.39375 17644.51800 
        931         932         933         934         935         936 
11501.50754 38129.46617 12387.41968  3583.54426 10225.35619 30060.82834 
        937         938         939         940         941         942 
12948.23914  5652.45954  8548.66424 30103.70092  5544.82136  3683.73967 
        943         944         945         946         947         948 
 5314.14921  3135.84628 28466.66148 30019.70412  7139.22213 13257.99812 
        949         950         951         952         953         954 
 9821.73252 34646.95226 13065.42012 35638.66926 33179.54599  7986.34531 
        955         956         957         958         959         960 
16443.63427 33455.22953 11386.92231  8694.11912 36519.59303  5587.89559 
        961         962         963         964         965         966 
 8400.93394 12274.37866  2728.63920  2832.33096 17576.40609  8492.11732 
        967         968         969         970         971         972 
10449.73616  -531.61826 30195.62628 36237.52679  3910.29007  6101.55422 
        973         974         975         976         977         978 
15295.23913 18600.86557 10020.48857 10482.32374 33649.58172 14409.37724 
        979         980         981         982         983         984 
 8175.04789 11102.11768 15754.79838  9923.94760  7061.16989  1440.74337 
        985         986         987         988         989         990 
 7765.02409 10935.44909  7265.82951   689.87502  7430.84688  4018.68829 
        991         992         993         994         995         996 
35326.35120 11266.34132  4532.57687 11254.43270  6830.92074  9313.92867 
        997         998         999        1000        1001        1002 
 5157.40986 13774.06373  9387.11423 15318.23138 34887.06908  3771.52146 
       1003        1004        1005        1006        1007        1008 
  758.22049  8662.11815 11338.54483 25828.15848 30223.29161  3773.35303 
       1009        1010        1011        1012        1013        1014 
 6519.42253  1176.68088  2897.14500  8449.89078 24906.10217 39824.31669 
       1015        1016        1017        1018        1019        1020 
11479.46601  7932.71906 16574.72849 28891.30909 13951.29228 25343.56174 
       1021        1022        1023        1024        1025        1026 
13274.21401 27731.66799 31722.04353  4154.77994  7814.90208  8270.58220 
       1027        1028        1029        1030        1031        1032 
 1619.59372   217.22024  1262.57948 37386.22830  3674.95154 -1312.51837 
       1033        1034        1035        1036        1037        1038 
11828.68087 25067.62114  9148.54816  8808.44097 12886.71547 27342.93902 
       1039        1040        1041        1042        1043        1044 
 6750.89052  8424.72128 25810.49856 11803.80833  -226.04209  4637.73245 
       1045        1046        1047        1048        1049        1050 
11954.06798  5268.21941  6326.99260  9174.09987 17835.81324 14322.26172 
       1051        1052        1053        1054        1055        1056 
12523.02085  7570.76488  6320.64726  3267.91783  5252.72343  8250.41274 
       1057        1058        1059        1060        1061        1062 
 2262.16127 31995.83248  6134.72827  3971.86769  6714.68183 35391.79941 
       1063        1064        1065        1066        1067        1068 
 9757.53638 16763.55104 13899.97197 28331.47022  4792.14261 15861.18236 
       1069        1070                                                 
17830.45856  4181.30312 13981.85035 12268.63225 21223.67580 40941.28540 
                                                                        
 5272.17580  9249.49520  9850.43200 13974.45555 31620.00106  2138.07070 
                                                                        
 1263.24900 43753.33705 21978.67690  3227.12110  4350.51440  9414.92000 
                                                                        
 3857.75925  3180.51010  4433.91590  2203.47185  8556.90700  2166.73200 
                                                                        
24667.41900 22192.43711 11085.58680 10825.25370  4931.64700 29330.98315 
                                                                        
 6373.55735 18838.70366  4320.41085 21195.81800  2534.39375  3645.08940 
                                                                        
 8062.76400 22462.04375 14256.19280  8334.58960 24059.68019 19361.99880 
                                                                        
38709.17600 22493.65964  2134.90150  1664.99960 18157.87600 10214.63600 
                                                                        
46661.44240  8428.06930  4753.63680 11381.32540 35147.52848 10226.28420 
                                                                        
 2639.04290  5227.98875  4399.73100  5383.53600  8782.46900  7173.35995 
                                                                        
40419.01910  1880.07000 14988.43200  9144.56500  9377.90470  8527.53200 
                                                                        
12574.04900  8671.19125  1967.02270  8023.13545  2494.02200 37484.44930 
                                                                        
 6082.40500  8444.47400 12629.89670  1633.04440  8269.04400  8825.08600 
                                                                        
 7045.49900  3443.06400  8823.98575  3062.50825 13429.03540  3956.07145 
                                                                        
 2136.88225  4237.12655  2755.02095  2257.47525  3021.80915 10976.24575 
                                                                        
33471.97189 46200.98510 18259.21600 11931.12525 23288.92840  5385.33790 
                                                                        
14692.66935  5972.37800 13770.09790  1694.79640 45702.02235  7201.70085 
                                                                        
21774.32215  9861.02500 10407.08585 10355.64100 32734.18630 13887.20400 
                                                                        
 5469.00660 41919.09700  3481.86800 16577.77950  2416.95500  3309.79260 
                                                                        
11881.96960  6079.67150  3935.17990 12032.32600 17178.68240  4137.52270 
                                                                        
 5080.09600 27218.43725 12231.61360 33732.68670  5855.90250  2302.30000 
                                                                        
15820.69900 11396.90020 17128.42608  6203.90175  3561.88890 23306.54700 
                                                                        
12557.60530 11743.29900 16450.89470 20009.63365 13063.88300 36837.46700 
                                                                        
23967.38305  7954.51700  6128.79745  7537.16390  3981.97680 13725.47184 
                                                                        
10704.47000  8627.54110 38245.59327 63770.42801  4922.91590  9583.89330 
                                                                        
12523.60480  2205.98080  6117.49450  4234.92700  3704.35450  7624.63000 
                                                                        
 2632.99200  6457.84340 40720.55105  7986.47525  4518.82625 11944.59435 
                                                                        
 2130.67590 27000.98473  7325.04820  5693.43050  1621.88270  2899.48935 
                                                                        
13393.75600  1743.21400 11093.62290  8615.30000 11289.10925 13844.79720 
                                                                        
 1875.34400  1253.93600 11326.71487 40273.64550  3500.61230  1632.03625 
                                                                        
 9869.81020 16069.08475 44423.80300 20296.86345  6067.12675  2597.77900 
                                                                        
 4795.65680 12982.87470  8413.46305  9625.92000  4894.75330  3353.28400 
                                                                        
16455.70785  1744.46500 10493.94580  1972.95000  4527.18295 15170.06900 
                                                                        
 2020.55230  3558.62025  6123.56880  4032.24070 40932.42950  6753.03800 
                                                                        
13415.03810  7228.21565 39047.28500 19539.24300  3176.28770  2150.46900 
                                                                        
12644.58900 19798.05455  7640.30920  5438.74910 23568.27200  6875.96100 
                                                                        
39611.75770 15817.98570 11082.57720 20462.99766  1837.28190 27724.28875 
                                                                        
 8124.40840 15828.82173 43943.87610 19040.87600  9447.25035 12265.50690 
                                                                        
 9504.31030  1242.26000 11674.13000  3410.32400 34779.61500 24603.04837 
                                                                        
 9957.72160  1646.42970 12475.35130  5969.72300  9500.57305  1241.56500 
                                                                        
39836.51900  8342.90875 28468.91901  6600.36100  2211.13075  6796.86325 
                                                                        
36085.21900  4435.09420 47305.30500 11244.37690  2219.44510 11840.77505 
                                                                        
11345.51900 34254.05335 10601.41200 39125.33225 24535.69855 17043.34140 
                                                                        
26140.36030  4661.28635  4564.19145 36124.57370 12129.61415  2680.94930 
                                                                        
12479.70895  1769.53165 12029.28670  8125.78450  6664.68595  7160.09400

names(results) <- c('predicted', 'actual')
results <- as.data.frame(t(results))
print(head(results, 40))

  predicted   actual       NA       NA      NA      NA       NA       NA
1  7857.807 25155.68 12265.71 7175.195 4176.87 8634.96 9915.097 33727.55
       NA       NA       NA       NA      NA       NA       NA       NA
1 6194.82 12158.22 3605.161 12877.23 5487.32 6366.702 31000.57 16611.12
        NA       NA       NA       NA       NA       NA      NA       NA
1 33924.24 13542.38 28592.22 3516.368 -1144.97 34498.62 33629.8 29790.85
        NA       NA       NA       NA       NA       NA       NA       NA
1 10047.41 5435.192 11712.74 6947.763 12249.08 6053.509 35596.88 4007.256
        NA       NA       NA       NA       NA       NA       NA       NA
1 4605.707 34230.32 31220.31 33633.17 30212.14 10305.27 11817.29 35799.25
        NA       NA       NA       NA       NA       NA       NA      NA
1 4776.905 3881.517 26218.58 7923.204 10883.09 5458.494 5347.229 26426.8
        NA       NA       NA       NA       NA       NA       NA       NA
1 8668.737 7844.454 10640.64 10858.95 41292.71 5957.169 1877.684 3914.299
        NA       NA       NA       NA       NA       NA       NA       NA
1 13897.32 31100.98 22860.84 15754.77 14012.92 5546.925 8121.507 8949.213
        NA       NA       NA       NA       NA       NA       NA       NA
1 14019.11 9630.269 17098.33 13774.94 8618.898 28502.75 3684.801 39005.46
        NA       NA       NA       NA       NA       NA       NA       NA
1 10518.83 28395.08 12497.04 1988.959 5606.055 4456.101 39310.64 6661.238
        NA       NA       NA       NA       NA       NA       NA       NA
1 2837.809 1899.554 31560.66 5382.136 29258.31 8210.812 13655.34 13249.61
        NA       NA       NA       NA       NA       NA       NA       NA
1 15168.95 12236.21 38668.18 28282.97 5443.899 3035.447 7147.588 13044.12
        NA       NA       NA       NA       NA       NA       NA      NA
1 9696.008 9003.543 1814.707 15051.96 10215.78 35589.86 10441.15 32124.1
        NA       NA       NA       NA       NA       NA       NA       NA
1 11695.93 2403.091 4497.293 10653.78 33979.86 8005.235 11167.54 14627.05
        NA       NA       NA       NA       NA       NA       NA       NA
1 17195.83 10514.62 35240.11 4331.985 11412.37 8765.869 3118.309 8570.626
        NA       NA       NA       NA       NA       NA       NA       NA
1 13227.27 12165.59 3395.226 6355.892 11076.95 14782.64 1993.815 4393.847
        NA       NA       NA       NA       NA       NA       NA       NA
1 12394.49 74.09649 9697.643 37082.33 14434.46 36107.07 14935.61 30831.83
        NA       NA      NA       NA       NA       NA     NA       NA
1 11703.46 10282.47 12004.4 16768.66 14444.81 6263.699 6566.2 7810.779
        NA       NA       NA       NA       NA      NA       NA       NA
1 8654.896 2199.291 34879.63 2551.738 3705.276 3412.36 15928.64 12522.79
       NA       NA       NA       NA       NA       NA      NA       NA
1 404.294 12532.22 2724.722 5519.807 37167.64 13038.44 927.389 8516.754
        NA       NA       NA    NA       NA       NA       NA       NA
1 11437.31 9050.997 11552.05 12863 11837.28 17091.72 9480.103 2758.338
        NA       NA       NA       NA       NA       NA       NA       NA
1 11931.91 13802.07 9414.086 9595.141 10483.74 224.0556 9899.388 4084.976
        NA       NA       NA       NA       NA      NA      NA       NA
1 12849.24 10575.72 5402.584 30846.46 17005.46 11680.7 13232.5 11011.72
       NA      NA       NA       NA       NA       NA       NA       NA
1 4780.56 38140.4 8964.055 9708.871 24280.42 32742.51 14546.18 7924.797
        NA       NA       NA       NA       NA       NA       NA       NA
1 32825.67 8435.407 11098.02 14983.35 38452.87 5488.116 26073.54 184.1584
        NA       NA       NA      NA      NA       NA       NA       NA
1 8829.707 8676.583 7565.803 27209.4 33152.6 3679.587 2891.108 8806.612
        NA       NA       NA       NA       NA       NA       NA       NA
1 13850.32 7062.826 15684.04 13278.77 11213.73 4285.011 13392.11 31123.72
        NA       NA       NA       NA       NA       NA       NA       NA
1 4449.337 4022.107 5302.028 28627.41 13361.53 27165.02 7257.548 28298.24
        NA       NA       NA       NA       NA       NA        NA       NA
1 32375.83 33488.57 13053.16 14770.64 29302.03 17304.85 -101.7755 7678.261
        NA       NA       NA       NA       NA       NA       NA       NA
1 32162.51 8877.979 7764.662 2505.838 9757.078 1825.005 1206.606 15901.91
        NA       NA       NA       NA       NA       NA       NA       NA
1 10296.51 28727.28 5881.485 436.8843 32440.77 3107.043 28305.93 4269.489
        NA       NA       NA       NA       NA       NA       NA       NA
1 15148.43 34722.63 9841.919 23262.75 6306.336 31015.89 5475.359 8328.095
        NA       NA       NA        NA       NA       NA       NA       NA
1 8320.063 4270.666 8086.726 -166.8557 11679.72 11156.71 11313.97 9759.323
        NA       NA       NA       NA       NA       NA       NA       NA
1 14781.47 11174.49 7131.107 4905.217 14413.77 8658.455 16597.92 11176.63
        NA       NA       NA      NA       NA       NA       NA       NA
1 5045.163 12421.42 28498.26 1097.63 11883.57 3722.377 8642.824 10190.32
        NA       NA       NA       NA       NA       NA       NA       NA
1 9127.336 9400.351 5443.929 9355.504 1064.909 7912.418 33707.98 3404.607
        NA       NA       NA       NA       NA       NA       NA       NA
1 9151.779 8126.915 12300.76 12281.69 13580.56 10249.99 5270.357 6111.354
        NA       NA       NA       NA       NA       NA       NA       NA
1 33782.24 1381.891 4426.521 16971.23 15484.64 2151.836 7447.597 28214.58
        NA       NA       NA       NA       NA        NA       NA       NA
1 26967.13 9753.474 30321.85 13169.01 2924.322 -954.3943 844.0963 6938.347
        NA       NA      NA       NA       NA       NA       NA       NA
1 7751.014 5348.193 38163.1 7865.986 2178.337 2616.891 6825.072 4130.587
        NA       NA       NA       NA       NA       NA       NA       NA
1 5555.264 10381.38 29396.34 10358.89 2252.751 37292.99 2339.423 7676.793
        NA       NA       NA       NA       NA       NA       NA       NA
1 2587.728 33093.89 4745.887 191.3874 5434.042 4780.802 7461.375 6126.256
        NA       NA       NA       NA       NA       NA       NA       NA
1 5681.059 1115.607 12995.62 4649.913 8794.959 36809.01 15924.97 7914.911
        NA      NA       NA       NA       NA       NA       NA       NA
1 5710.073 2182.22 24999.46 32779.38 1793.749 37277.77 10551.49 5743.365
        NA      NA       NA       NA       NA       NA       NA       NA
1 5436.827 8207.26 14770.07 15128.83 11256.29 25906.16 7141.208 14088.79
        NA       NA       NA       NA       NA       NA       NA       NA
1 7973.589 29638.13 6915.073 6401.452 8225.661 8214.019 5290.954 9689.889
        NA       NA       NA       NA       NA       NA       NA       NA
1 5765.177 4118.788 7804.801 11147.16 10451.94 14878.28 11595.39 15854.18
        NA       NA       NA       NA      NA       NA       NA       NA
1 39186.06 35434.37 27809.52 8650.313 1227.14 34569.09 8227.418 8878.757
        NA       NA       NA       NA       NA       NA       NA      NA
1 11118.56 9166.206 39139.16 8867.181 9111.256 35167.54 2210.316 12712.4
        NA      NA       NA       NA       NA       NA       NA       NA
1 1948.933 14134.2 39520.26 11082.68 28221.55 6379.907 11335.25 32472.57
        NA       NA       NA       NA       NA       NA       NA       NA
1 5673.915 35622.68 12639.91 5509.078 36026.96 9590.309 11006.81 33904.13
        NA       NA       NA       NA       NA       NA       NA       NA
1 7054.076 5063.984 12674.63 9617.589 3159.166 1573.895 36388.07 6471.232
        NA       NA       NA       NA       NA       NA       NA    NA
1 12712.95 10682.14 12002.41 34261.26 10607.37 6828.882 7008.798 13149
        NA      NA       NA       NA      NA      NA       NA       NA
1 11843.24 11614.1 12665.19 8022.183 9636.86 6360.14 11438.34 8455.515
        NA       NA       NA       NA       NA       NA       NA       NA
1 15194.03 12882.66 9463.651 2209.449 33547.14 15284.58 3588.821 31666.75
        NA       NA       NA       NA       NA       NA       NA       NA
1 11001.19 32474.49 13711.04 11018.24 15515.03 6565.372 28756.19 11316.48
        NA       NA       NA       NA       NA      NA       NA       NA
1 6303.432 14910.56 8850.306 8617.885 1857.964 6627.58 4191.012 11924.16
        NA       NA      NA       NA       NA       NA       NA       NA
1 7282.304 10406.66 9991.78 12913.81 8883.721 5744.449 9776.394 3736.568
       NA       NA       NA       NA       NA       NA       NA       NA
1 8259.53 3413.937 28057.09 31312.77 5076.958 27250.49 10622.75 9823.619
        NA       NA       NA       NA       NA       NA       NA       NA
1 3663.619 36186.38 9156.873 5367.716 27704.77 7645.984 307.4098 26164.24
        NA       NA       NA       NA       NA       NA       NA       NA
1 11388.24 3638.086 30788.99 7295.428 2467.725 12775.09 11427.55 8858.335
        NA       NA       NA       NA       NA       NA       NA       NA
1 7964.103 14981.53 14872.77 30912.34 12625.48 5783.664 3677.766 12429.54
        NA       NA       NA       NA       NA       NA       NA       NA
1 15609.01 13170.55 28826.41 3001.423 14671.81 29351.79 8254.878 12901.38
        NA       NA       NA       NA       NA       NA       NA       NA
1 10457.07 11019.99 26333.79 5689.458 7057.762 10257.64 5071.312 8931.753
        NA       NA       NA      NA    NA       NA       NA       NA
1 11891.31 10902.24 6926.116 15400.3 13118 13802.26 3957.068 26767.25
        NA       NA       NA       NA       NA       NA       NA       NA
1 12313.19 6165.694 35056.31 3269.117 6780.725 32670.06 12648.94 14422.17
        NA       NA       NA       NA       NA      NA       NA       NA
1 11817.87 12684.59 10671.62 5032.127 11801.49 29982.7 3992.612 4484.209
     NA       NA       NA       NA       NA       NA       NA       NA
1 32026 4941.642 398.3945 2160.223 12336.57 10622.69 422.8156 4436.001
       NA       NA       NA       NA       NA       NA       NA       NA
1 6391.97 4708.431 38014.03 12097.62 8235.012 10906.29 10517.86 10666.15
        NA       NA       NA       NA       NA      NA       NA       NA
1 39703.81 9872.818 6720.748 11093.44 31431.59 6859.97 16859.93 3444.133
       NA       NA        NA       NA       NA       NA       NA      NA
1 13243.1 14763.88 -87.93788 32162.26 7583.861 30981.95 2081.438 12385.3
        NA       NA       NA       NA      NA       NA       NA       NA
1 7213.326 27435.04 8076.807 1636.957 11237.2 35839.27 8974.941 4598.056
        NA       NA       NA       NA       NA       NA       NA       NA
1 32431.68 9643.345 9316.632 12807.52 1771.775 39305.16 -1090.51 15475.26
        NA       NA       NA       NA       NA       NA      NA       NA
1 9191.653 14850.34 3176.099 6633.121 7604.072 5382.706 11875.7 3071.272
        NA       NA       NA       NA       NA       NA       NA      NA
1 16239.32 26957.18 6948.471 11732.38 7388.102 5682.439 10540.82 9867.57
         NA       NA       NA       NA       NA       NA       NA       NA
1 -31.36893 29002.73 31026.54 39292.26 36741.75 7514.932 12254.67 6351.002
        NA       NA       NA       NA       NA       NA      NA       NA
1 34851.78 12893.37 41834.91 24792.22 5295.879 5122.862 4629.59 9516.138
        NA      NA       NA       NA       NA       NA      NA       NA
1 15043.84 29271.4 16446.53 5569.935 27550.79 11369.24 11748.9 10507.25
        NA       NA       NA       NA      NA       NA       NA       NA
1 9094.041 10527.75 3210.712 10465.11 7258.27 12406.99 15811.63 39487.17
        NA        NA       NA       NA       NA       NA       NA       NA
1 25905.13 -1742.708 12524.21 39426.24 3794.337 39203.42 6177.657 12933.75
        NA       NA       NA       NA       NA       NA       NA       NA
1 4231.174 7803.976 12160.33 8505.444 1588.156 1475.546 32952.74 14089.26
        NA       NA       NA       NA       NA       NA        NA       NA
1 3316.342 3906.874 36582.53 27917.39 11871.64 7154.073 -1516.761 2800.301
        NA       NA       NA       NA       NA       NA       NA       NA
1 1924.194 14201.11 9554.747 5649.104 6051.587 1968.203 5041.529 14942.74
        NA       NA       NA       NA       NA       NA       NA       NA
1 16532.36 4233.173 12464.26 3007.518 7345.242 9636.396 37660.87 32827.38
        NA       NA      NA       NA       NA       NA       NA       NA
1 4590.324 8735.927 35236.2 4886.725 25444.94 9391.724 16842.25 15234.76
        NA       NA       NA       NA       NA       NA       NA       NA
1 9218.837 8434.724 3420.459 3133.248 9885.899 13000.77 2032.429 6887.245
        NA       NA       NA       NA       NA      NA       NA       NA
1 10180.09 6529.181 2916.918 35906.64 6124.235 12976.5 8732.698 30556.13
        NA       NA       NA       NA       NA       NA       NA       NA
1 10502.36 4155.585 6746.996 3262.362 9098.894 6854.451 14757.77 10832.72
        NA       NA     NA      NA       NA       NA    NA       NA
1 26463.58 12020.86 4037.7 26806.2 7928.818 972.6665 12793 16738.24
        NA       NA       NA      NA       NA       NA       NA       NA
1 31273.55 13756.27 6450.136 25315.5 13975.08 15202.15 4201.128 12048.46
        NA       NA        NA       NA       NA       NA       NA       NA
1 11359.91 23778.97 -495.8204 12086.86 6379.046 7455.724 28838.25 35715.45
        NA       NA       NA       NA       NA       NA      NA       NA
1 3994.349 3137.613 34710.02 9073.559 14441.22 31434.57 10908.1 10420.79
        NA       NA       NA      NA      NA       NA       NA       NA
1 11884.63 32722.01 8012.603 9588.73 23596.7 14916.65 36082.55 14993.82
        NA       NA       NA       NA    NA       NA       NA      NA
1 3169.771 1924.107 11009.56 39833.43 11115 12435.21 12691.64 4694.06
        NA       NA       NA      NA       NA       NA       NA       NA
1 13433.93 6467.607 3511.224 12793.5 2827.436 12738.58 11567.07 1183.328
        NA       NA       NA        NA       NA       NA       NA       NA
1 11299.29 12617.09 1386.376 -654.5799 6839.075 9096.856 26750.24 14660.57
        NA       NA       NA       NA       NA       NA       NA       NA
1 18900.81 33170.31 8680.107 7630.157 8319.605 6240.171 23699.65 26980.42
        NA       NA      NA       NA       NA       NA       NA        NA
1 37613.17 16271.81 12129.3 38777.21 6381.118 14903.89 23351.81 -1999.607
        NA       NA       NA       NA       NA       NA       NA       NA
1 2762.483 10672.59 27442.71 15537.98 6621.601 8612.198 3221.825 8694.406
        NA       NA       NA       NA       NA       NA       NA       NA
1 10573.21 29596.04 38183.44 3929.986 13159.88 11183.36 30524.46 15946.91
        NA       NA       NA       NA       NA       NA       NA       NA
1 4414.308 13556.44 12482.83 17421.45 9506.709 3497.905 27456.01 14742.69
        NA       NA       NA       NA       NA      NA       NA       NA
1 12516.12 2304.872 14374.85 8039.309 875.0007 6585.97 27175.15 9686.755
        NA      NA     NA       NA    NA       NA       NA       NA
1 7052.645 7106.11 4095.6 7677.404 32837 3070.918 27839.42 25599.83
        NA       NA      NA      NA       NA       NA      NA       NA
1 13519.25 4597.457 6721.73 4218.69 78.50513 7122.251 7695.44 9212.737
        NA       NA       NA      NA       NA       NA       NA       NA
1 356.7415 42101.38 6231.725 7112.28 6425.675 10093.08 12163.56 11562.66
        NA       NA      NA       NA       NA       NA        NA       NA
1 35111.29 39572.47 39865.3 7596.073 39495.58 4143.943 -553.2371 14649.21
        NA       NA      NA       NA       NA       NA       NA       NA
1 14057.84 34731.19 10279.9 26733.45 5880.023 3997.208 5190.893 8422.653
        NA       NA       NA       NA      NA       NA       NA       NA
1 11576.04 13498.01 35026.44 27624.51 5590.14 11415.08 35700.35 7139.924
        NA      NA       NA       NA       NA       NA       NA       NA
1 712.8033 11539.6 5765.709 13052.05 40381.57 8716.457 10194.32 9253.047
        NA       NA      NA       NA       NA       NA      NA       NA
1 12097.12 11676.02 7377.84 15533.48 29803.77 11680.39 2765.41 2192.223
        NA       NA       NA       NA       NA       NA       NA      NA
1 200.7923 15142.64 6145.258 3799.153 29961.95 9339.476 3253.925 13954.2
        NA       NA       NA       NA       NA       NA       NA       NA
1 10293.27 2225.704 14460.26 15160.02 8039.686 8568.277 2943.521 9594.295
        NA       NA       NA       NA       NA       NA       NA       NA
1 12966.64 11746.11 6136.359 9348.042 8918.074 33177.56 2980.881 10484.63
        NA       NA       NA       NA       NA       NA       NA       NA
1 2060.544 9271.454 4934.289 1889.796 27950.49 15036.85 10080.78 14555.31
        NA       NA       NA       NA       NA       NA       NA       NA
1 13781.49 10357.31 12137.89 5756.886 2186.288 11077.45 31900.13 38030.75
        NA       NA       NA       NA      NA       NA      NA       NA
1 9157.183 10324.76 12295.45 35802.48 27520.4 5077.709 1763.83 37823.84
        NA       NA       NA       NA       NA       NA       NA       NA
1 9252.394 17644.52 11501.51 38129.47 12387.42 3583.544 10225.36 30060.83
        NA      NA       NA      NA       NA      NA       NA       NA
1 12948.24 5652.46 8548.664 30103.7 5544.821 3683.74 5314.149 3135.846
        NA      NA       NA    NA       NA       NA       NA       NA
1 28466.66 30019.7 7139.222 13258 9821.733 34646.95 13065.42 35638.67
        NA       NA       NA       NA       NA       NA       NA       NA
1 33179.55 7986.345 16443.63 33455.23 11386.92 8694.119 36519.59 5587.896
        NA       NA       NA       NA       NA       NA       NA        NA
1 8400.934 12274.38 2728.639 2832.331 17576.41 8492.117 10449.74 -531.6183
        NA       NA      NA       NA       NA       NA       NA       NA
1 30195.63 36237.53 3910.29 6101.554 15295.24 18600.87 10020.49 10482.32
        NA       NA       NA       NA      NA       NA      NA       NA
1 33649.58 14409.38 8175.048 11102.12 15754.8 9923.948 7061.17 1440.743
        NA       NA      NA      NA       NA       NA       NA       NA
1 7765.024 10935.45 7265.83 689.875 7430.847 4018.688 35326.35 11266.34
        NA       NA       NA       NA      NA       NA       NA       NA
1 4532.577 11254.43 6830.921 9313.929 5157.41 13774.06 9387.114 15318.23
        NA       NA       NA       NA       NA       NA       NA       NA
1 34887.07 3771.521 758.2205 8662.118 11338.54 25828.16 30223.29 3773.353
        NA       NA       NA       NA      NA       NA       NA       NA
1 6519.423 1176.681 2897.145 8449.891 24906.1 39824.32 11479.47 7932.719
        NA       NA       NA       NA       NA       NA       NA      NA
1 16574.73 28891.31 13951.29 25343.56 13274.21 27731.67 31722.04 4154.78
        NA       NA       NA       NA       NA       NA       NA        NA
1 7814.902 8270.582 1619.594 217.2202 1262.579 37386.23 3674.952 -1312.518
        NA       NA       NA       NA       NA       NA       NA       NA
1 11828.68 25067.62 9148.548 8808.441 12886.72 27342.94 6750.891 8424.721
       NA       NA        NA       NA       NA       NA       NA     NA
1 25810.5 11803.81 -226.0421 4637.732 11954.07 5268.219 6326.993 9174.1
        NA       NA       NA       NA       NA       NA       NA       NA
1 17835.81 14322.26 12523.02 7570.765 6320.647 3267.918 5252.723 8250.413
        NA       NA       NA       NA       NA      NA       NA       NA
1 2262.161 31995.83 6134.728 3971.868 6714.682 35391.8 9757.536 16763.55
        NA       NA       NA       NA       NA       NA       NA       NA
1 13899.97 28331.47 4792.143 15861.18 17830.46 4181.303 13981.85 12268.63
        NA       NA       NA       NA       NA       NA    NA       NA
1 21223.68 40941.29 5272.176 9249.495 9850.432 13974.46 31620 2138.071
        NA       NA       NA       NA       NA      NA       NA      NA
1 1263.249 43753.34 21978.68 3227.121 4350.514 9414.92 3857.759 3180.51
        NA       NA       NA       NA       NA       NA       NA       NA
1 4433.916 2203.472 8556.907 2166.732 24667.42 22192.44 11085.59 10825.25
        NA       NA       NA      NA       NA       NA       NA       NA
1 4931.647 29330.98 6373.557 18838.7 4320.411 21195.82 2534.394 3645.089
        NA       NA       NA      NA       NA    NA       NA       NA
1 8062.764 22462.04 14256.19 8334.59 24059.68 19362 38709.18 22493.66
        NA   NA       NA       NA       NA       NA       NA       NA
1 2134.901 1665 18157.88 10214.64 46661.44 8428.069 4753.637 11381.33
        NA       NA       NA       NA       NA       NA       NA      NA
1 35147.53 10226.28 2639.043 5227.989 4399.731 5383.536 8782.469 7173.36
        NA      NA       NA       NA       NA       NA       NA       NA
1 40419.02 1880.07 14988.43 9144.565 9377.905 8527.532 12574.05 8671.191
        NA       NA       NA       NA       NA       NA      NA       NA
1 1967.023 8023.135 2494.022 37484.45 6082.405 8444.474 12629.9 1633.044
        NA       NA       NA       NA       NA       NA       NA       NA
1 8269.044 8825.086 7045.499 3443.064 8823.986 3062.508 13429.04 3956.071
        NA       NA       NA       NA       NA       NA       NA       NA
1 2136.882 4237.127 2755.021 2257.475 3021.809 10976.25 33471.97 46200.99
        NA       NA       NA       NA       NA       NA      NA       NA
1 18259.22 11931.13 23288.93 5385.338 14692.67 5972.378 13770.1 1694.796
        NA       NA       NA       NA       NA       NA       NA      NA
1 45702.02 7201.701 21774.32 9861.025 10407.09 10355.64 32734.19 13887.2
        NA      NA       NA       NA       NA       NA       NA       NA
1 5469.007 41919.1 3481.868 16577.78 2416.955 3309.793 11881.97 6079.672
       NA       NA       NA       NA       NA       NA       NA       NA
1 3935.18 12032.33 17178.68 4137.523 5080.096 27218.44 12231.61 33732.69
        NA     NA      NA      NA       NA       NA       NA       NA
1 5855.903 2302.3 15820.7 11396.9 17128.43 6203.902 3561.889 23306.55
        NA      NA       NA       NA       NA       NA       NA       NA
1 12557.61 11743.3 16450.89 20009.63 13063.88 36837.47 23967.38 7954.517
        NA       NA       NA       NA       NA       NA       NA       NA
1 6128.797 7537.164 3981.977 13725.47 10704.47 8627.541 38245.59 63770.43
        NA       NA      NA       NA       NA       NA       NA      NA
1 4922.916 9583.893 12523.6 2205.981 6117.494 4234.927 3704.354 7624.63
        NA       NA       NA       NA       NA       NA       NA       NA
1 2632.992 6457.843 40720.55 7986.475 4518.826 11944.59 2130.676 27000.98
        NA       NA       NA       NA       NA       NA       NA     NA
1 7325.048 5693.431 1621.883 2899.489 13393.76 1743.214 11093.62 8615.3
        NA      NA       NA       NA       NA       NA       NA       NA
1 11289.11 13844.8 1875.344 1253.936 11326.71 40273.65 3500.612 1632.036
       NA       NA      NA       NA       NA       NA       NA       NA
1 9869.81 16069.08 44423.8 20296.86 6067.127 2597.779 4795.657 12982.87
        NA      NA       NA       NA       NA       NA       NA      NA
1 8413.463 9625.92 4894.753 3353.284 16455.71 1744.465 10493.95 1972.95
        NA       NA       NA      NA       NA       NA       NA       NA
1 4527.183 15170.07 2020.552 3558.62 6123.569 4032.241 40932.43 6753.038
        NA       NA       NA       NA       NA       NA       NA       NA
1 13415.04 7228.216 39047.29 19539.24 3176.288 2150.469 12644.59 19798.05
        NA       NA       NA       NA       NA       NA       NA    NA
1 7640.309 5438.749 23568.27 6875.961 39611.76 15817.99 11082.58 20463
        NA       NA       NA       NA       NA       NA      NA       NA
1 1837.282 27724.29 8124.408 15828.82 43943.88 19040.88 9447.25 12265.51
       NA      NA       NA       NA       NA       NA       NA      NA
1 9504.31 1242.26 11674.13 3410.324 34779.61 24603.05 9957.722 1646.43
        NA       NA       NA       NA       NA       NA       NA       NA
1 12475.35 5969.723 9500.573 1241.565 39836.52 8342.909 28468.92 6600.361
        NA       NA       NA       NA       NA       NA       NA       NA
1 2211.131 6796.863 36085.22 4435.094 47305.31 11244.38 2219.445 11840.78
        NA       NA       NA       NA      NA       NA       NA       NA
1 11345.52 34254.05 10601.41 39125.33 24535.7 17043.34 26140.36 4661.286
        NA       NA       NA       NA       NA       NA       NA       NA
1 4564.191 36124.57 12129.61 2680.949 12479.71 1769.532 12029.29 8125.784
        NA       NA
1 6664.686 7160.094

Here is the actual and predicted cost of healthcare cost for the training samples using the linear regression model.

It looks like the accuracy is ok but is not the best. We will move on to look at Classification trees model to see if we can make better predictions.

mse <- mean(((results$actual) - (results$predicted))^2)
print(mse)

[1] 299216501

#root mean squared error
print(mse^0.5)

[1] 17297.88

SSE <- sum((results$actual - results$predicted)^2)
print(SSE)

[1] 299216501

#are there any NA values 
any(is.na(healthcare))

[1] FALSE

#look at structure "str"
str(healthcare)

Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame':    1338 obs. of  8 variables:
 $ age_yrs     : num  18 43 62 49 46 63 41 55 52 25 ...
 $ gender      : chr  "female" "female" "male" "female" ...
 $ body_mass   : num  42.2 30.7 37.4 23.2 40.4 ...
 $ no_children : num  0 2 0 2 2 0 3 2 0 0 ...
 $ smoker      : chr  "yes" "no" "no" "no" ...
 $ region      : chr  "southeast" "northwest" "southwest" "northwest" ...
 $ prev_balance: num  -17938 195 -4273 1480 -671 ...
 $ costs       : num  38793 8311 12979 10157 8733 ...
 - attr(*, "spec")=
  .. cols(
  ..   age_yrs = col_double(),
  ..   gender = col_character(),
  ..   body_mass = col_double(),
  ..   no_children = col_double(),
  ..   smoker = col_character(),
  ..   region = col_character(),
  ..   prev_balance = col_double(),
  ..   costs = col_double()
  .. )

library(ggplot2)
library(ggthemes)
library(dplyr)
library(corrplot)

corrplot 0.84 loaded

library(corrgram)
num.cols <- sapply(healthcare,is.numeric)

cor.data<- cor(healthcare[,num.cols])
print(cor.data)

                age_yrs  body_mass no_children prev_balance      costs
age_yrs      1.00000000 0.10927188  0.04246900   0.07003449 0.29900819
body_mass    0.10927188 1.00000000  0.01275890   0.01443067 0.19834097
no_children  0.04246900 0.01275890  1.00000000   0.01405894 0.06799823
prev_balance 0.07003449 0.01443067  0.01405894   1.00000000 0.06350883
costs        0.29900819 0.19834097  0.06799823   0.06350883 1.00000000

There shows a small correlation between ages vs costs of healthcare and BMI vs cost of healthcare.

print(corrplot(cor.data, method='color'))

                age_yrs  body_mass no_children prev_balance      costs
age_yrs      1.00000000 0.10927188  0.04246900   0.07003449 0.29900819
body_mass    0.10927188 1.00000000  0.01275890   0.01443067 0.19834097
no_children  0.04246900 0.01275890  1.00000000   0.01405894 0.06799823
prev_balance 0.07003449 0.01443067  0.01405894   1.00000000 0.06350883
costs        0.29900819 0.19834097  0.06799823   0.06350883 1.00000000

There shows a small correlation between ages vs costs of healthcare and BMI vs cost of healthcare.

corrgram(healthcare)

corrgram(healthcare,order=TRUE, lower.panel=panel.shade,
         upper.panel=panel.pie, text.panel=panel.txt)

ggplot(healthcare,aes(x=costs)) + geom_histogram(bins=50,alpha=0.5,fill='blue')

res<- residuals(mdl)
class(res)

[1] "numeric"

Calculating the Residual Mean

res<- as.data.frame(res)
head(res)

         res
1 10397.6082
2 -1769.9442
3 -2222.7893
4   982.6833
5 -5241.8527
6 -3033.1766

mean(healthcare$costs)==mean(fitted.values(mdl))

[1] FALSE

mean(residuals(mdl))

[1] 8.068417e-14

plot out the residuals:

good residual the mean=0 we want the source of residual to be random we want the predicted to = the actual value

ggplot(res,aes(res))+ geom_histogram(fill='blue', alpha=0.5, bins = 40)

###The residuals are around 0 and spread out. a few residual small peak is on both sides zero.

summary(mdl)


Call:
lm(formula = costs ~ ., data = healthcare)

Residuals:
   Min     1Q Median     3Q    Max 
-11671  -2862  -1018   1393  29499 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.187e+04  9.870e+02 -12.023  < 2e-16 ***
age_yrs          2.551e+02  1.191e+01  21.424  < 2e-16 ***
gendermale      -8.097e+01  3.333e+02  -0.243 0.808079    
body_mass        3.384e+02  2.856e+01  11.847  < 2e-16 ***
no_children      4.722e+02  1.376e+02   3.431 0.000619 ***
smokeryes        2.383e+04  4.127e+02  57.747  < 2e-16 ***
regionnorthwest -3.655e+02  4.756e+02  -0.769 0.442292    
regionsoutheast -1.030e+03  4.780e+02  -2.154 0.031410 *  
regionsouthwest -9.838e+02  4.774e+02  -2.061 0.039518 *  
prev_balance     7.932e-02  3.619e-02   2.192 0.028539 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6053 on 1328 degrees of freedom
Multiple R-squared:  0.7518,    Adjusted R-squared:  0.7501 
F-statistic:   447 on 9 and 1328 DF,  p-value: < 2.2e-16

Classification and Regression Tree model for the Healthcare data set to determine cost of healthcare.

Tree model maybe a better model to predict and determine the cost of healthcare.

Model interpretability is makes predictions easier in Tree Classification

Model performance of trees have superior performance compared to other ML algorithm.

library("rpart")
library("rpart.plot")
#look at data 
str(healthcare)

Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame':    1338 obs. of  8 variables:
 $ age_yrs     : num  18 43 62 49 46 63 41 55 52 25 ...
 $ gender      : chr  "female" "female" "male" "female" ...
 $ body_mass   : num  42.2 30.7 37.4 23.2 40.4 ...
 $ no_children : num  0 2 0 2 2 0 3 2 0 0 ...
 $ smoker      : chr  "yes" "no" "no" "no" ...
 $ region      : chr  "southeast" "northwest" "southwest" "northwest" ...
 $ prev_balance: num  -17938 195 -4273 1480 -671 ...
 $ costs       : num  38793 8311 12979 10157 8733 ...
 - attr(*, "spec")=
  .. cols(
  ..   age_yrs = col_double(),
  ..   gender = col_character(),
  ..   body_mass = col_double(),
  ..   no_children = col_double(),
  ..   smoker = col_character(),
  ..   region = col_character(),
  ..   prev_balance = col_double(),
  ..   costs = col_double()
  .. )

#create the model
healthcare_model<- rpart(formula= gender ~ ., 
                         data=healthcare, 
                         method= "class")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

###Cost of Male and female health care in the classification tree. We can follow the tree to determine how each feature effects healthcare price for each individual. ###Here younger males in north with less then 32 BMI pay less than females.

Here we look at how smokers effect on the price of healthcare cost.

#create the model
healthcare_model<- rpart(formula= smoker ~ ., 
                         data=healthcare, 
                         method= "class")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

###Here is a smoker classification Tree. Smokers pay more but have less then 30 BMI

Here we look at the different region of patients paying for healthcare costs.

Here is a classification on region an body mass.

#create the model
healthcare_model<- rpart(formula= region ~ ., 
                         data=healthcare, 
                         method= "class")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

###People in Southeast are the larger in weight and have a BMI greater than 33. Northeast there are a lot of patients who are less than 19 year old. Northwest have patients mostly around 19-20.Northeast and northwest have patients with that are greater or equal to 20 years old. In the Northeast most patients have a BMI less than 24 while Northwest patients have a BMI greater than 24.

This Regression tree is looking at the Age of the patients in the model.

#create the model
healthcare_model<- rpart(formula= age_yrs ~ ., 
                         data=healthcare, 
                         method= "anova")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

###Here is a regression tree looking at the age and comparing it to the body mass and cost of health care for each patient. It looks like those who smoke and have large BMI and are older pay more in healthcare cost.

This Regression tree is looking at the BMI of the patients in the model.

#create the model
healthcare_model<- rpart(formula= body_mass ~ ., 
                         data=healthcare, 
                         method= "anova")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

###Smokers have a lower body mass. BMI abive 31 who are smokers pay over 33K in healthcare cost. Patients with BMI over 36 pay 36K in healthcare cost.

This Regression tree is looking at the number of children patient’s have in the model.

#create the model
healthcare_model<- rpart(formula= no_children ~ ., 
                         data=healthcare, 
                         method= "anova")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

### Here you can follow the tree and determing the cost of healthcare by the number of children you have.

This Regression tree is looking at the previous balance of the patients in the model.

#create the model
healthcare_model<- rpart(formula= prev_balance ~ ., 
                         data=healthcare, 
                         method= "anova")

#Display the results
rpart.plot(x=healthcare_model, yesno =2, type = 0, extra = 0)

how many rows are in the data

n <- nrow(healthcare)
n

[1] 1338

#rows
nrow(health_train)

[1] 1070

#calculate 80% of the rows
n_train <- round(0.80 * n)
n_train

[1] 1070

set.seed(123)
#create an index that is 80% of the data
train_ind <- sample(1:n, n_train)

#seperate the trian protion 
health_train <- healthcare[train_ind,]

#see if it worked but counting 

#using the "-" sign seperate the test portion 
health_test <-  healthcare[-train_ind,]

Follow down the Tree:

handle both numerical and categorical feature input can handle missing data elegantly robost to outlier requires little data preparation can model non linear data

high variance cause model poor performance

#train the model to predict the  binary response, "costs"
healthcare_coststrain <- rpart(formula = region ~.,
                          data=health_train,
                          method="class")
rpart.plot(x=healthcare_coststrain, yesno =2, type = 0, extra = 0)

print(healthcare_coststrain)

n= 1070 

node), split, n, loss, yval, (yprob)
      * denotes terminal node

  1) root 1070 766 southeast (0.24766355 0.22803738 0.28411215 0.24018692)  
    2) body_mass< 32.9825 696 496 northeast (0.28735632 0.27155172 0.20402299 0.23706897)  
      4) age_yrs< 18.5 33  14 northeast (0.57575758 0.00000000 0.42424242 0.00000000) *
      5) age_yrs>=18.5 663 474 northwest (0.27300151 0.28506787 0.19306184 0.24886878)  
       10) age_yrs>=19.5 622 441 northeast (0.29099678 0.26848875 0.20418006 0.23633441)  
         20) body_mass< 23.58 113  64 northeast (0.43362832 0.23893805 0.14159292 0.18584071) *
         21) body_mass>=23.58 509 369 northwest (0.25933202 0.27504912 0.21807466 0.24754420)  
           42) costs>=8948.072 269 182 northeast (0.32342007 0.26394052 0.18959108 0.22304833) *
           43) costs< 8948.072 240 171 northwest (0.18750000 0.28750000 0.25000000 0.27500000)  
             86) gender=male 118  76 northwest (0.22881356 0.35593220 0.16949153 0.24576271) *
             87) gender=female 122  82 southeast (0.14754098 0.22131148 0.32786885 0.30327869)  
              174) body_mass>=27.71 78  47 southeast (0.16666667 0.19230769 0.39743590 0.24358974) *
              175) body_mass< 27.71 44  26 southwest (0.11363636 0.27272727 0.20454545 0.40909091) *
       11) age_yrs< 19.5 41  19 northwest (0.00000000 0.53658537 0.02439024 0.43902439) *
    3) body_mass>=32.9825 374 212 southeast (0.17379679 0.14705882 0.43315508 0.24598930) *

#train the model to predict the  binary response, "costs"
healthcare_coststrain <- rpart(formula = gender ~.,
                          data=health_train,
                          method="class")
rpart.plot(x=healthcare_coststrain, yesno =2, type = 0, extra = 0)

print(healthcare_coststrain)

n= 1070 

node), split, n, loss, yval, (yprob)
      * denotes terminal node

    1) root 1070 531 male (0.4962617 0.5037383)  
      2) costs>=1997.439 996 481 female (0.5170683 0.4829317)  
        4) costs< 29793.37 865 396 female (0.5421965 0.4578035)  
          8) age_yrs< 20.5 58  17 female (0.7068966 0.2931034) *
          9) age_yrs>=20.5 807 379 female (0.5303594 0.4696406)  
           18) prev_balance>=718.3705 295 123 female (0.5830508 0.4169492) *
           19) prev_balance< 718.3705 512 256 female (0.5000000 0.5000000)  
             38) body_mass< 23.6775 65  23 female (0.6461538 0.3538462)  
               76) prev_balance< -38.75311 49  12 female (0.7551020 0.2448980) *
               77) prev_balance>=-38.75311 16   5 male (0.3125000 0.6875000) *
             39) body_mass>=23.6775 447 214 male (0.4787472 0.5212528)  
               78) prev_balance>=-3164.895 384 191 female (0.5026042 0.4973958)  
                156) prev_balance< -2388.678 37  12 female (0.6756757 0.3243243) *
                157) prev_balance>=-2388.678 347 168 male (0.4841499 0.5158501)  
                  314) prev_balance>=-2279.908 339 168 male (0.4955752 0.5044248)  
                    628) body_mass>=27.4775 262 124 female (0.5267176 0.4732824)  
                     1256) body_mass< 27.8325 9   1 female (0.8888889 0.1111111) *
                     1257) body_mass>=27.8325 253 123 female (0.5138340 0.4861660)  
                       2514) region=northeast,southeast 138  59 female (0.5724638 0.4275362) *
                       2515) region=northwest,southwest 115  51 male (0.4434783 0.5565217)  
                         5030) body_mass>=32.49 60  24 female (0.6000000 0.4000000)  
                          10060) age_yrs< 53.5 49  15 female (0.6938776 0.3061224) *
                          10061) age_yrs>=53.5 11   2 male (0.1818182 0.8181818) *
                         5031) body_mass< 32.49 55  15 male (0.2727273 0.7272727) *
                    629) body_mass< 27.4775 77  30 male (0.3896104 0.6103896) *
                  315) prev_balance< -2279.908 8   0 male (0.0000000 1.0000000) *
               79) prev_balance< -3164.895 63  21 male (0.3333333 0.6666667) *
        5) costs>=29793.37 131  46 male (0.3511450 0.6488550) *
      3) costs< 1997.439 74  16 male (0.2162162 0.7837838) *

#train the model to predict the  binary response, "costs"
healthcare_coststrain <- rpart(formula = smoker ~.,
                          data=health_train,
                          method="class")
rpart.plot(x=healthcare_coststrain, yesno =2, type = 0, extra = 0)

print(healthcare_coststrain)

n= 1070 

node), split, n, loss, yval, (yprob)
      * denotes terminal node

 1) root 1070 220 no (0.79439252 0.20560748)  
   2) costs< 15294.71 789   8 no (0.98986058 0.01013942) *
   3) costs>=15294.71 281  69 yes (0.24555160 0.75444840)  
     6) costs< 32328.5 157  66 yes (0.42038217 0.57961783)  
      12) body_mass>=30.01 40   0 no (1.00000000 0.00000000) *
      13) body_mass< 30.01 117  26 yes (0.22222222 0.77777778)  
        26) costs>=24453.36 35  15 yes (0.42857143 0.57142857)  
          52) age_yrs< 52.5 15   5 no (0.66666667 0.33333333) *
          53) age_yrs>=52.5 20   5 yes (0.25000000 0.75000000) *
        27) costs< 24453.36 82  11 yes (0.13414634 0.86585366) *
     7) costs>=32328.5 124   3 yes (0.02419355 0.97580645) *

Predicting class labels for test data

class_prediction <- predict(object=healthcare_coststrain,
                            newdata = health_test,
                            type = "class")

                                                     
print(class_prediction)

  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
 no  no yes yes  no  no  no  no  no  no  no yes yes  no  no  no  no  no 
 19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36 
 no  no  no  no  no yes  no  no  no yes  no yes  no yes  no  no  no yes 
 37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54 
 no  no  no yes yes yes  no  no yes  no yes  no  no  no yes  no  no  no 
 55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72 
 no  no  no  no yes  no  no  no  no  no  no  no  no  no  no yes  no  no 
 73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90 
 no  no  no  no  no  no  no  no  no  no  no  no  no  no  no  no yes yes 
 91  92  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107 108 
yes  no yes  no  no  no  no  no yes  no yes  no  no  no yes  no  no yes 
109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 
 no yes  no  no  no  no  no  no yes  no  no yes  no yes  no  no yes  no 
127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 
 no  no  no yes  no  no yes yes  no yes yes  no  no  no  no  no  no  no 
145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 
yes yes  no  no  no  no  no  no  no  no  no  no yes  no  no  no  no  no 
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 
 no  no  no  no  no  no  no  no  no  no  no  no  no yes  no  no  no  no 
181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 
yes yes  no  no  no  no  no  no  no  no  no  no  no  no  no  no  no  no 
199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 
 no  no yes  no  no  no yes yes  no  no  no yes  no  no yes  no yes yes 
217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 
 no  no  no  no  no yes yes yes  no  no  no  no  no  no yes  no  no  no 
235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 
 no  no  no  no yes  no  no  no  no  no yes  no yes  no  no  no  no yes 
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 
 no yes  no yes  no  no  no yes  no  no  no  no  no  no  no  no 
Levels: no yes

Slit to Training/Testing/Validation with three sets for Regression Tree

# Look at the data
str(healthcare)

Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame':    1338 obs. of  8 variables:
 $ age_yrs     : num  18 43 62 49 46 63 41 55 52 25 ...
 $ gender      : chr  "female" "female" "male" "female" ...
 $ body_mass   : num  42.2 30.7 37.4 23.2 40.4 ...
 $ no_children : num  0 2 0 2 2 0 3 2 0 0 ...
 $ smoker      : chr  "yes" "no" "no" "no" ...
 $ region      : chr  "southeast" "northwest" "southwest" "northwest" ...
 $ prev_balance: num  -17938 195 -4273 1480 -671 ...
 $ costs       : num  38793 8311 12979 10157 8733 ...
 - attr(*, "spec")=
  .. cols(
  ..   age_yrs = col_double(),
  ..   gender = col_character(),
  ..   body_mass = col_double(),
  ..   no_children = col_double(),
  ..   smoker = col_character(),
  ..   region = col_character(),
  ..   prev_balance = col_double(),
  ..   costs = col_double()
  .. )

# Set seed and create assignment 
set.seed(1)
assignment <- sample(1:3, size = nrow(healthcare), prob = c(0.7, 0.15, 0.15), replace = TRUE)

# Create a train, validation and tests from the original data frame 
costs_train <- healthcare[assignment == 1, ]  # subset grade to training indices only
costs_valid <- healthcare[assignment == 2, ]  # subset grade to validation indices only
costs_test <- healthcare[assignment == 3, ]   # subset grade to test indices only

Training with Regression Tree

# Train the model
costs_model <- rpart(formula = costs ~ ., 
                     data = costs_train, 
                     method = "anova")

# Look at the model output                      
print(costs_model)

n= 935 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 935 145503000000 13463.960  
   2) smoker=no 737  27519870000  8372.520  
     4) age_yrs< 44.5 444   9898037000  5531.242  
       8) prev_balance>=-2987.364 434   7934463000  5241.341  
        16) prev_balance< 2675.865 417   5768731000  4867.923 *
        17) prev_balance>=2675.865 17    681280900 14401.050 *
       9) prev_balance< -2987.364 10    344100800 18112.970 *
     5) age_yrs>=44.5 293   8605910000 12678.070 *
   3) smoker=yes 198  27764810000 32415.420  
     6) body_mass< 30.01 94   2789057000 21585.910 *
     7) body_mass>=30.01 104   3987441000 42203.640 *

# Plot the tree model
rpart.plot(x = costs_model, yesno = 2, type = 0, extra = 0)

Predict the cost for all the people in the test set Evaluate model based on test set RMSE Room Mean Square Error.RMSE tells us approximately how far away our predictions are from the true values

library(caret)

Loading required package: lattice


Attaching package: 'lattice'

The following object is masked from 'package:corrgram':

    panel.fill


Attaching package: 'caret'

The following object is masked from 'package:purrr':

    lift

# Generate predictions on a test set
pred <- predict(object = costs_model,  # model object 
                newdata = costs_test)  # test dataset

# Compute the RMSE
RMSE <- function(error) { sqrt(mean(error^2)) }
#RMSE(actual = costs_test$costs, 
#     predicted = pred)

RMSE <- function(error) { sqrt(mean(error^2)) }
RMSE(costs_test$costs)

[1] 17093.09

mae <- function(error) { mean(abs(error)) }
mae(costs_test$costs)

[1] 12887.8

rmse1 <- mean((costs_test$costs - pred)^2)
print(rmse1)

[1] 13941695

#root mean squared error
print(rmse1^0.5)

[1] 3733.858

Tuning model: Tune model using prune() function by finding best ‘CP’ complexity parameter

# Plot the "CP Table" matrix of info on optimal pruning
plotcp(costs_model)

# Print the "CP Table" 
print(costs_model$cptable)

          CP nsplit rel error    xerror       xstd
1 0.62004448      0 1.0000000 1.0017461 0.06153153
2 0.14424656      1 0.3799555 0.3832674 0.02310000
3 0.06196382      2 0.2357090 0.2398942 0.01743371
4 0.01113017      3 0.1737451 0.1812306 0.01561988
5 0.01020220      4 0.1626150 0.1850294 0.01615821
6 0.01000000      5 0.1524128 0.1816746 0.01588088

# Retrieve optimal cp value based on cross-validated error
opt_index <- which.min(costs_model$cptable[, "xerror"])
cp_opt <- costs_model$cptable[opt_index, "CP"]

# Prune the model (to optimized cp value) trim off least important splits based on CP
costs_model_opt <- prune(tree = costs_model, 
                         cp = cp_opt)
                          
# Plot the optimized model
rpart.plot(x = costs_model_opt, yesno = 2, type = 0, extra = 0)

###Prune function provides the optimal prunings based on the cp value. We prune the tree to avoid any overfitting of the data. The convention is to have a small tree and the one with least cross validated error given by print() function i.e. ‘xerror’. Plotcp() provides a graphical representation to the cross validated error summary. The cp values are plotted against the geometric mean to depict the deviation until the minimum value is reached. The default value of the cp is .01. In the table is shows that 4 splits will give use the best decision tree and avoiding any overfitting of the data.

These are the 4 splits the decision tree gave us after using the training model and pruning it shown in the diagram above. The decision tree after pruning shows that 4 price values. 1. Patients who are non smoker, younger than 45 pay around $5531 for healthcare cost. 2. Patients who are non smoker, older than 45 pay around $13,000 for healthcare cost. 3. Patients who are smoker, BMI less than 30 pay around $22,000 for healthcare cost. 4. Patients who are smoker, BMI greater than 30 pay around $42,000 for healthcare cost.

Generate grid of hyperparameter values uinge expand.grid() to generate grid of maxdepth and minsplit values

# Establish a list of possible values for minsplit and maxdepth
minsplit <- seq(1, 4, 1)
maxdepth <- seq(1, 6, 1)

# Create a data frame containing all combinations 
hyper_grid <- expand.grid(minsplit = minsplit, maxdepth = maxdepth)

# Check out the grid
head(hyper_grid)

  minsplit maxdepth
1        1        1
2        2        1
3        3        1
4        4        1
5        1        2
6        2        2

# Print the number of grid combinations
nrow(hyper_grid)

[1] 24

Generate grid models

write look to train grid of models and store models in list

# Number of potential models in the grid
num_models <- nrow(hyper_grid)

# Create an empty list to store models
costs_models1 <- list()

# Write a loop over the rows of hyper_grid to train the grid of models
for (i in 1:num_models) {

    # Get minsplit, maxdepth values at row i
    minsplit <- hyper_grid$minsplit[i]
    maxdepth <- hyper_grid$maxdepth[i]

    # Train a model and store in the list
    costs_models1[[i]] <- rpart(formula = costs ~ ., 
                               data = costs_train, 
                               method = "anova",
                               minsplit = minsplit,
                               maxdepth = maxdepth)
}

Evaluate the grid

split healthcare dataset into training, validating and test earlier. Validation set used to evaluate performace of model and used to compare the performace of a group of models with goal of choosing “best model”. Once I have best model, final estimate of performance is computed on test set. Test set should only ever be used to estimate model performance and should not be used in model selection.

library(broom)
# Number of potential models in the grid
num_models <- length(costs_models1)

# Create an empty vector to store RMSE values
rmse_values <- c()

# Write a loop over the models to compute validation RMSE
for (i in 1:num_models) {

    # Retrieve the i^th model from the list
    model <- costs_models1[[i]]
    
    # Generate predictions on grade_valid 
    pred <- predict(object = model,
                    newdata = costs_valid)
    
    #Compute validation RMSE and add to the 
RMSE <- function(error) { sqrt(mean(error^2)) }
rmse_values[i] <- RMSE(costs_valid$costs) 
rmse_values[i]                     
}

# Function for Root Mean Squared Error
RMSE <- function(error) { sqrt(mean(error^2)) }
RMSE(costs_valid$costs)

[1] 16939.14

RMSE(costs_test$costs)  #RMSE(fit$residuals)

[1] 17093.09

# Function for Mean Absolute Error
mae <- function(error) { mean(abs(error)) }
mae(costs_valid$costs)

[1] 12753.34

mae(costs_test$costs)

[1] 12887.8

# Identify the model with smallest validation set RMSE
best_model <- costs_models1[[which.min(rmse_values)]]

# Print the model paramters of the best model
best_model$control

$minsplit
[1] 1

$minbucket
[1] 0

$cp
[1] 0.01

$maxcompete
[1] 4

$maxsurrogate
[1] 5

$usesurrogate
[1] 2

$surrogatestyle
[1] 0

$maxdepth
[1] 1

$xval
[1] 10

# Compute test set RMSE on best_model
pred <- predict(object = best_model,
              newdata = costs_test)
RMSE <- function(error) { sqrt(mean(error^2)) }

RMSE_best_model <- RMSE(costs_test$costs)
RMSE_best_model

[1] 17093.09

After the Hyperparameter the best fit model for the Regression tree Predicts that the predicted cost for Healthcare is $3910.80

*****************Test***************

# R^2 and adjusted R^2
#summary(mdl)

# add random noise
healthcare_noisy <- healthcare %>%
  mutate(noise = rnorm(nrow(healthcare)))
  
# compute new model
mdl2 <- lm(costs ~ body_mass + smoker + age_yrs +no_children +noise, data = healthcare_noisy)

# new R^2 and adjusted R^2
summary(mdl2)


Call:
lm(formula = costs ~ body_mass + smoker + age_yrs + no_children + 
    noise, data = healthcare_noisy)

Residuals:
     Min       1Q   Median       3Q      Max 
-11899.1  -2892.0   -967.9   1474.1  29868.5 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -12142.22     942.04 -12.889  < 2e-16 ***
body_mass      323.02      27.38  11.798  < 2e-16 ***
smokeryes    23818.78     411.10  57.939  < 2e-16 ***
age_yrs        257.82      11.89  21.680  < 2e-16 ***
no_children    473.38     137.74   3.437 0.000607 ***
noise          243.03     171.77   1.415 0.157343    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6066 on 1332 degrees of freedom
Multiple R-squared:  0.7501,    Adjusted R-squared:  0.7491 
F-statistic: 799.5 on 5 and 1332 DF,  p-value: < 2.2e-16

# return a vector
predict(mdl2)

           1            2            3            4            5 
30345.217057  9657.116538 15822.390773  8879.803494 13493.228333 
           6            7            8            9           10 
15524.551167 10602.605802 13692.864275 13901.927703  2684.502250 
          11           12           13           14           15 
14988.798696 32155.741463  5831.717362 10235.408397 13972.037024 
          16           17           18           19           20 
 5683.889069  8607.188676 10114.735423 34675.552428  6902.513541 
          21           22           23           24           25 
14176.807951 13610.814512  6877.509934  9438.211795 10119.858566 
          26           27           28           29           30 
34718.160457 14479.362075  4265.401659 11872.234799 34713.675685 
          31           32           33           34           35 
 3492.251204  3511.812875 31637.603116 14067.431909 37075.643233 
          36           37           38           39           40 
 7342.411391 33284.394993 13540.536915 14413.327099 24382.602527 
          41           42           43           44           45 
40045.243087 13887.706868 16509.216941   307.016941  5075.374966 
          46           47           48           49           50 
 3954.346417  4024.546526 37565.113661 11533.867490  1933.821476 
          51           52           53           54           55 
 4555.186288  7194.863054  2682.301831 13170.489277 35810.332284 
          56           57           58           59           60 
13691.268322  5950.352690  8644.113018 30929.932011 11513.973000 
          61           62           63           64           65 
 8073.163944  1657.296447  1304.201791 35853.142986  8791.757361 
          66           67           68           69           70 
 7670.809599 13182.525546  4216.327849 33489.507147 32407.205596 
          71           72           73           74           75 
25440.483701  3257.708941 23466.057193  4153.603479 16203.557119 
          76           77           78           79           80 
13549.819866  5681.856257 11319.011039  8776.573970  5902.079956 
          81           82           83           84           85 
 6123.741815 10951.679231  9946.652586 27446.104259 10758.236438 
          86           87           88           89           90 
 5943.723619  6154.070332 11498.486068 15267.172410  4561.646863 
          91           92           93           94           95 
 9394.817189  2439.365608 34765.549099 13588.136495  5806.263822 
          96           97           98           99          100 
 5933.630729  1310.317533 33335.308977 12820.525162 38075.269566 
         101          102          103          104          105 
 2119.619403 17258.655328 10049.172860  3828.461944  9968.260401 
         106          107          108          109          110 
12076.077726  6737.274583  1984.292001 11207.790136 12626.409608 
         111          112          113          114          115 
 4464.229172  7282.414861 28593.071403 14779.322105  6464.883850 
         116          117          118          119          120 
14188.128171  8391.905272  8219.688418 34710.993171 38560.184311 
         121          122          123          124          125 
 2556.060185  5891.553290 12133.805692  5234.314138  4458.329760 
         126          127          128          129          130 
34569.684971  8346.449218 36916.327716 28601.363224  4235.801283 
         131          132          133          134          135 
10603.470266  2419.936973 11582.055589  8420.387972 10762.942954 
         136          137          138          139          140 
 -723.838601 30160.292883 13101.707884 10621.168457  7028.138627 
         141          142          143          144          145 
 8216.189634 15638.071420 16868.557306  2424.033375  9160.600002 
         146          147          148          149          150 
 4612.178913  9842.050045 36857.134316 11771.434938 30253.807602 
         151          152          153          154          155 
10918.454503 10391.908729 10961.327615  6436.981131 39657.445657 
         156          157          158          159          160 
31538.841676  6007.021198  5873.838568 16445.635694  9365.662154 
         161          162          163          164          165 
 8973.472691 31039.062524  3245.547402 13842.117352  6240.558080 
         166          167          168          169          170 
 7212.562484 31229.829447 11763.470548   471.279788 12339.209926 
         171          172          173          174          175 
 8150.501535 12436.092915 31994.873246 25696.277778  4349.995577 
         176          177          178          179          180 
  546.190545 40174.801073  6830.736201  5826.643476  4598.172379 
         181          182          183          184          185 
 8314.136549  8720.753537  8849.699557  3759.416982 11594.986862 
         186          187          188          189          190 
 5013.872610  2087.209068  4466.503671  6132.773888  9962.820411 
         191          192          193          194          195 
10297.049289  1287.398976  6001.706815  7013.604922  7539.839681 
         196          197          198          199          200 
30180.489122 12960.662419 11058.295640 10552.415948 33714.425361 
         201          202          203          204          205 
34555.559235 32041.676714  6636.921129 10597.356778 12053.000431 
         206          207          208          209          210 
29569.227115 12956.119925  2552.983515 10864.919278  4038.910108 
         211          212          213          214          215 
 8276.885133  2643.715879 10266.207518  1627.164007  9525.593367 
         216          217          218          219          220 
12764.825407  3623.334383  9946.372789 11843.439804  7472.918476 
         221          222          223          224          225 
 3765.568706  4303.260480  7969.475117  7374.841913 29677.715895 
         226          227          228          229          230 
11305.792050  2570.082682  3187.161711 15698.703090 32554.864823 
         231          232          233          234          235 
 6966.234026  2693.231989  3992.481549 13366.413335 39284.898424 
         236          237          238          239          240 
15234.322130  2605.320232  9211.493079  6037.298465 23953.272465 
         241          242          243          244          245 
 7517.739388 22906.531756  1976.176970 10699.972238  4895.035675 
         246          247          248          249          250 
12470.386346  4969.423409  2262.592359 25545.466722  2523.614020 
         251          252          253          254          255 
 5319.049112 28602.481662  5793.691257 35521.650624 28042.037744 
         256          257          258          259          260 
36497.921527 13317.460722  8023.941431  2185.707240 10153.209455 
         261          262          263          264          265 
11816.318167 38844.245405  6739.955618 30797.703109  4735.287847 
         266          267          268          269          270 
10072.914777 28860.281712  6656.054121  9646.424779 10732.736513 
         271          272          273          274          275 
18887.886166  8458.931783 12557.409401 27110.136895  7424.813314 
         276          277          278          279          280 
 2666.462118 11562.680092 14745.933907  2460.749028  8817.178857 
         281          282          283          284          285 
12182.488054 11146.559008 10291.639605 10954.881257  9660.466896 
         286          287          288          289          290 
35491.588846 14353.018389  7429.791075  -647.471317 14306.014171 
         291          292          293          294          295 
32243.144574  8085.719358  4095.515959  3308.713986 12946.430415 
         296          297          298          299          300 
15271.509465 26661.131624  5473.382634 15515.910579  5643.577043 
         301          302          303          304          305 
35763.207509  5539.873747  6742.347179 11480.877213 11316.952019 
         306          307          308          309          310 
 9338.982306  1910.037688  6037.316626 36668.970295  6481.942120 
         311          312          313          314          315 
14119.017608  9767.007188 12080.651562  2075.178620 13354.042012 
         316          317          318          319          320 
13885.233737  7883.711163  9448.330177  5817.396571 12276.381942 
         321          322          323          324          325 
 6422.318504 17251.041355 33553.491719 35833.701618  3153.515658 
         326          327          328          329          330 
33065.727880 11373.421163  6328.741440 13846.420949 10252.655556 
         331          332          333          334          335 
13104.692493 12598.669760 11064.334568 12197.663785 17842.488962 
         336          337          338          339          340 
 5479.194116  9440.784460  9530.396136 30050.974181 16737.936080 
         341          342          343          344          345 
 1161.747720 33074.006232 11988.052547  8812.202713  1984.459068 
         346          347          348          349          350 
 3146.399704  4161.751395 30477.471044  6198.946002  9967.611490 
         351          352          353          354          355 
 9391.189745 11577.924172 28575.500345  8441.810778  4845.137773 
         356          357          358          359          360 
14421.170781  7909.338510 30233.682157  9814.614807 13200.465036 
         361          362          363          364          365 
 7680.145994 10885.759153  9326.862391 36791.305213  8481.581711 
         366          367          368          369          370 
40069.902538  8263.382891  2595.774437  7598.781619 14006.885213 
         371          372          373          374          375 
 3771.791478  5329.253278 11450.968247 13657.378767  3902.735884 
         376          377          378          379          380 
 5224.712880  7608.671671  8144.113305 12070.793840 10604.412997 
         381          382          383          384          385 
 7580.318047  6365.387176  5715.760486  5803.495058  7193.837457 
         386          387          388          389          390 
10812.265500  9962.769629  4893.611044 13384.669223 12611.594553 
         391          392          393          394          395 
14094.572562  8502.013668 15336.842119 11959.958970  4027.487247 
         396          397          398          399          400 
13579.230850 12778.182953 16631.511377  7300.603280 11049.158348 
         401          402          403          404          405 
 1045.496714  4687.621088 29797.538528 25735.129799  9384.676512 
         406          407          408          409          410 
 6259.246663  9633.926834 29284.134288  7572.157824  4671.765333 
         411          412          413          414          415 
25711.000084 35041.055385  3659.315479 11811.178303  3547.633655 
         416          417          418          419          420 
 7559.698313  9560.602259 10914.942350  5972.349459  9674.422182 
         421          422          423          424          425 
15494.198191  7378.455011  6380.910316  4176.458076  7943.767853 
         426          427          428          429          430 
29589.609072  8863.707436  4582.796815  5121.517813  6320.485905 
         431          432          433          434          435 
10001.078885 14204.021987 28794.205046   782.627626  2281.839127 
         436          437          438          439          440 
29868.437534  5560.074074  3154.486151  2403.458515 32882.225910 
         441          442          443          444          445 
12382.501134  -405.526673 22919.971208 39246.441605  5453.321752 
         446          447          448          449          450 
26040.310467 15731.151325 39123.754470 12031.817304 12270.344419 
         451          452          453          454          455 
13281.444934 14428.312371 37604.480617 15282.321065 38170.382069 
         456          457          458          459          460 
13204.515828 34281.116955  -428.195230  4344.554508 11694.317181 
         461          462          463          464          465 
  951.475691  5046.913202 28689.079946  7845.626566 37345.559602 
         466          467          468          469          470 
 8911.184173  2315.114786 11058.418523  3728.341929  9117.674326 
         471          472          473          474          475 
12122.064712  4140.334370  5868.379966  5459.124689  8112.311692 
         476          477          478          479          480 
15012.898305 10513.208909  8341.118412 15738.994456  5198.596193 
         481          482          483          484          485 
13151.869923 14518.406274 11831.321030  4982.406543 12022.661111 
         486          487          488          489          490 
-2713.135800  4478.785664 26321.582173 30354.384913  8469.872869 
         491          492          493          494          495 
 6038.726891 38047.178069  7251.902818  8512.485774  3436.320160 
         496          497          498          499          500 
31117.348057  9939.350493 28068.459002  6687.999031   749.049988 
         501          502          503          504          505 
 6287.382669 27176.650447 11288.081196  7825.654029 10088.448474 
         506          507          508          509          510 
33711.258886  -352.241856  5467.287262 11232.427951  7824.888817 
         511          512          513          514          515 
26496.708764  9008.490614 11511.944959 10277.948306 11443.044139 
         516          517          518          519          520 
33909.140868 12120.407562  7452.458942 37596.583835  9187.502396 
         521          522          523          524          525 
30872.878159  5040.870839 26871.046924 15270.309875 31140.806170 
         526          527          528          529          530 
16172.682870 17017.542928 39468.072621  6612.158501  7319.635512 
         531          532          533          534          535 
14898.739362 13144.413146  6317.955144 14606.457439 25649.373679 
         536          537          538          539          540 
 7131.442995 25663.168218  3910.613351  6227.423435  9110.923372 
         541          542          543          544          545 
28184.094270  9119.148903  9414.467991 17113.211444  8713.970099 
         546          547          548          549          550 
 1957.752377 11694.142826 11125.438075  3468.689393 36687.424849 
         551          552          553          554          555 
35298.576354  4066.066395 32827.085756  2210.344383 39278.704259 
         556          557          558          559          560 
11635.258244  8270.003599 12344.040772 28214.810632 31996.120362 
         561          562          563          564          565 
 1681.956431 26827.284757  -318.968845  9287.189655 14182.821527 
         566          567          568          569          570 
 9931.606458 11609.733928 10512.771412  3139.922688 10378.781378 
         571          572          573          574          575 
 9937.867737 11871.241769  8452.038228  6024.534928  5351.070374 
         576          577          578          579          580 
 4888.784805 29081.249507  9288.424914  1482.186888  7044.445469 
         581          582          583          584          585 
 3278.427349  6791.378540  8968.441239  2867.979217 26963.288449 
         586          587          588          589          590 
 1816.480193 13282.241416  7527.503111  7208.059555  2731.009379 
         591          592          593          594          595 
12792.302286 11971.352707  5365.193798  4154.961807 32104.504063 
         596          597          598          599          600 
12282.741112  -520.263270  5981.628672 13874.136458 31532.546903 
         601          602          603          604          605 
11842.037674 13485.843082 31981.356666 11190.919869 10988.767762 
         606          607          608          609          610 
26105.720899 11927.704942  4396.099890 12636.720328 10177.485348 
         611          612          613          614          615 
10341.161474 14723.509197  7775.071878  7641.414336  9524.135985 
         616          617          618          619          620 
10797.431131 36465.646029 25795.352506 11266.339186  4300.528043 
         621          622          623          624          625 
11488.017573 15155.630361 33841.003600 10240.246507 11752.398423 
         626          627          628          629          630 
 4395.149551 17700.970623 15958.152817 12307.230478  1651.499954 
         631          632          633          634          635 
27706.447143 35564.548059  4835.856863 13935.040526 14030.324476 
         636          637          638          639          640 
26538.941828  4835.501587  1172.773194 36460.855850 12095.416220 
         641          642          643          644          645 
27719.787027 14564.123000  1272.380349 12858.000212  6466.186973 
         646          647          648          649          650 
 -444.995194 11478.782116 17201.990453 28137.724674  9854.656128 
         651          652          653          654          655 
 7629.529017 27507.850509   877.207756 37425.695014 12221.152494 
         656          657          658          659          660 
13732.479645 10719.744213 29781.573639 10266.126352  6317.180560 
         661          662          663          664          665 
 2261.075095 10043.225447   -85.887126  7303.381430  5117.948300 
         666          667          668          669          670 
12050.092452  1282.152311 27231.359943 10057.237744  4526.887124 
         671          672          673          674          675 
 9709.103698 11094.555088  7905.170759  6848.877792 30728.631917 
         676          677          678          679          680 
12288.639943 36250.895023  3001.871797 29786.842681 33608.209740 
         681          682          683          684          685 
26439.571360  8241.214206 13583.548397  7832.605878  5114.012508 
         686          687          688          689          690 
 4903.986208  1595.714701  9555.507700 37375.506281 11537.803693 
         691          692          693          694          695 
25180.053155 11592.348824  6861.521171    -7.254616  2467.182970 
         696          697          698          699          700 
 6760.042228 29680.536679  4065.614555  5285.426475  5614.533376 
         701          702          703          704          705 
18086.748318 31054.111297  4648.111264  9333.781904 27986.024776 
         706          707          708          709          710 
16013.173484  2554.976729 14650.832235 15773.188731  8839.107277 
         711          712          713          714          715 
11967.909144  3529.973106 10366.490220 11747.881754  2580.336563 
         716          717          718          719          720 
12583.606691  8065.223038  4088.399427  3340.730806  4917.220933 
         721          722          723          724          725 
 2792.653107 33799.817342 15021.360341 10517.520600  8422.688975 
         726          727          728          729          730 
10862.196340 29225.681035  2447.470642 34081.604666  2691.984390 
         731          732          733          734          735 
 8485.191815  7379.956785 16293.016687  5315.592495  9127.759691 
         736          737          738          739          740 
 9694.751575  2037.979663  5178.849568  8578.215403  5844.418457 
         741          742          743          744          745 
11921.981533  6700.911008 10427.114281 12959.897153 25288.671655 
         746          747          748          749          750 
37967.609395 12076.311793 15435.777690  9573.105972 11301.618491 
         751          752          753          754          755 
 5542.281766 14057.774244  5680.091814 31240.789097 28742.257568 
         756          757          758          759          760 
 2883.641511 11247.858083  8311.716955  6012.227983  5777.250170 
         761          762          763          764          765 
36286.728591 40885.134563  8583.126679  6497.706302 11628.545846 
         766          767          768          769          770 
28553.653361  9488.213700 12192.527815  4910.352360  7361.090045 
         771          772          773          774          775 
 9668.118561 11050.731697  5032.667317 -2051.187097 15718.167107 
         776          777          778          779          780 
29370.667634 14786.593786 10889.729327  7641.931530  2787.664443 
         781          782          783          784          785 
 6099.438193   878.625224  5348.836767  4379.329791  6770.660336 
         786          787          788          789          790 
12132.409589 32417.096748 31392.775551 16660.473265 13710.383731 
         791          792          793          794          795 
 9261.493286  3511.953775 26555.764352 30915.209453  6229.319290 
         796          797          798          799          800 
19103.030808  3179.622510 39400.465733  5479.660243 34742.598280 
         801          802          803          804          805 
 7772.333452 11361.954681  9155.855653  5790.414840  3989.928987 
         806          807          808          809          810 
 3200.916526  8126.612026  7507.341695 10916.035730 35426.935037 
         811          812          813          814          815 
10829.826361 14907.341429  6876.194826  5236.450863 28481.316597 
         816          817          818          819          820 
 9061.521771 34816.277357  3377.575281 13416.628968 29397.025230 
         821          822          823          824          825 
 7887.415724  7710.266086 26895.805363 13759.129791 12406.225447 
         826          827          828          829          830 
11881.640802 31075.908958  6004.747246  5305.516148 15433.890764 
         831          832          833          834          835 
12919.706777  6796.827137  7805.789497 14091.677029   583.332501 
         836          837          838          839          840 
 3220.520590  3151.095660  9939.057792  4341.125555  1515.422454 
         841          842          843          844          845 
 7329.064533 11370.852438 33744.479272  9924.812875 14537.160305 
         846          847          848          849          850 
 8229.919789  7370.612506 12519.786452  6835.866235 40360.352263 
         851          852          853          854          855 
13785.185908  6935.234468 18498.115784 12393.981678  3061.300644 
         856          857          858          859          860 
 9213.335773  9431.473621  3318.932470  2659.403928 37120.771320 
         861          862          863          864          865 
 9932.125914  9703.804252  5238.239674 14834.646625 40458.804068 
         866          867          868          869          870 
10833.284774 28675.901694  9959.150355  2100.604787     7.894474 
         871          872          873          874          875 
 3079.655219  9299.277097 15657.382836  4270.212270  6278.292259 
         876          877          878          879          880 
 7524.843220 11269.392505 18186.928043  9670.333632 12642.001148 
         881          882          883          884          885 
 9775.574116  1872.833712 36084.341158 13038.448449  3373.960420 
         886          887          888          889          890 
16016.662469 14336.824636 36202.093147 37308.624820  2548.452324 
         891          892          893          894          895 
 1815.749097 38841.004438 14715.936276  6254.805536 10736.682023 
         896          897          898          899          900 
10353.883207   570.382563 33394.505185  5692.495808 10678.663774 
         901          902          903          904          905 
 6252.244822 12976.027521  5051.406914 25863.137007  3289.183010 
         906          907          908          909          910 
 7286.971889  8050.877237 34191.447697  7529.521152  4282.839605 
         911          912          913          914          915 
 2626.704105  7326.658881 34194.999764  9116.327884  3470.073218 
         916          917          918          919          920 
 1006.599103   892.911262  7774.613312  3102.478669  5758.608773 
         921          922          923          924          925 
10581.182377  7622.514952 10835.533788 32724.354996  6281.490115 
         926          927          928          929          930 
 4715.544779  2428.107404 12715.293190 15729.311630  1978.763669 
         931          932          933          934          935 
 5959.036576  9167.304118 10239.114699 12816.988202 15449.096312 
         936          937          938          939          940 
37458.216429   565.761711  7151.019521 29877.774736  6599.053077 
         941          942          943          944          945 
 2105.054246 10945.831503  9680.336797  8411.039428 10951.921533 
         946          947          948          949          950 
32356.453937 16340.921848  7091.791361  3437.259103 11154.272795 
         951          952          953          954          955 
10616.412489 35824.735635  4726.675427 11713.639844  5139.553030 
         956          957          958          959          960 
31368.932773  4335.746204  5401.314483 10566.053607 10135.156478 
         961          962          963          964          965 
28774.932811 13636.523659  6578.122766 -1398.469094 32411.568434 
         966          967          968          969          970 
12117.697399   759.603850  3336.858959 15340.700928 15450.885471 
         971          972          973          974          975 
10106.762908  9975.534794 16917.539517  8287.874162 15108.162989 
         976          977          978          979          980 
24905.664146  4177.016790  9460.491540 10727.661478 17824.314653 
         981          982          983          984          985 
33348.544505  2618.087283 39382.809466 10271.051440  2766.090315 
         986          987          988          989          990 
14417.984598   707.077112 30664.533861  4785.353363  5289.645280 
         991          992          993          994          995 
 5140.992977 27588.338484  2499.112237  3455.875523 10454.332626 
         996          997          998          999         1000 
32883.638473 11506.878418  3271.024594  9479.884796 15581.266209 
        1001         1002         1003         1004         1005 
35959.512072   883.229678  5590.456165  6999.418858 11452.525675 
        1006         1007         1008         1009         1010 
13772.463961  9987.175973 11365.021794  8427.777285  9884.349094 
        1011         1012         1013         1014         1015 
18088.408130  1644.906346  4427.842393  2334.429065  4725.056836 
        1016         1017         1018         1019         1020 
17150.105463  5139.143046 11853.499929  2757.532377 11219.485554 
        1021         1022         1023         1024         1025 
 3254.228018  9126.586678  6805.755817 31192.061269 14088.722229 
        1026         1027         1028         1029         1030 
 7023.114762  6395.346836 39372.783292 28219.884951  3807.488075 
        1031         1032         1033         1034         1035 
17443.347785 11349.172610 13551.660174  8651.413172  -440.724355 
        1036         1037         1038         1039         1040 
34693.397559 32169.778472 13440.692921 34051.067425 33493.230080 
        1041         1042         1043         1044         1045 
12421.039061 -1552.964854  3903.659652 11230.992665 13840.573630 
        1046         1047         1048         1049         1050 
10119.303049  1519.345848 27858.289429  5895.132674  4531.751250 
        1051         1052         1053         1054         1055 
24146.999456  9156.579470 32473.644242 24532.893770 15300.336890 
        1056         1057         1058         1059         1060 
 5276.102575 31265.597775  4365.536628 29316.709494  8354.941652 
        1061         1062         1063         1064         1065 
 5572.311516 29691.758431  8129.967925  1429.119003  1402.494188 
        1066         1067         1068         1069         1070 
34709.045506 30027.214193 31576.118480 15775.026722 11420.288021 
        1071         1072         1073         1074         1075 
12079.662336 11435.252347 11809.025821 27190.635944  4798.018012 
        1076         1077         1078         1079         1080 
37813.933863 13439.136037  6651.864980 11949.165450 14867.387714 
        1081         1082         1083         1084         1085 
 9740.413584  1119.961691  8310.693523 30465.861220  1458.271563 
        1086         1087         1088         1089         1090 
 8868.884178 34979.149595 31550.041988 11484.715291  3540.113428 
        1091         1092         1093         1094         1095 
24505.479010 37902.287877 36158.773539  3037.945866  9261.112026 
        1096         1097         1098         1099         1100 
30165.964995 33326.962088  1982.761724 11051.379864 27605.955302 
        1101         1102         1103         1104         1105 
 9884.323068 12431.198057 15043.291724  3092.021263 37834.988273 
        1106         1107         1108         1109         1110 
 8305.283122  1622.167949 16169.646017 15299.534094 32159.554565 
        1111         1112         1113         1114         1115 
 5146.086161  9055.275581 14794.509649 14753.668846  3326.616382 
        1116         1117         1118         1119         1120 
 5838.647385  4720.232462 13580.596857 26043.802310 11080.277178 
        1121         1122         1123         1124         1125 
39980.030204  5492.013213  5313.880923 13545.865431 10961.912351 
        1126         1127         1128         1129         1130 
 8581.699556  4222.221597 15032.257952  3018.136532 33027.533259 
        1131         1132         1133         1134         1135 
 3820.887988 32483.622820 10705.254171  5666.150590  7078.225202 
        1136         1137         1138         1139         1140 
 5048.918849 12208.759456 41368.071961  9583.366505   246.368060 
        1141         1142         1143         1144         1145 
30586.941050  7233.921288 29624.949490 11224.881788  9029.749500 
        1146         1147         1148         1149         1150 
23617.197359 36517.677525 31233.553473 11627.924906 26890.052441 
        1151         1152         1153         1154         1155 
14441.178071  2482.446827 13975.653056    29.332582 30794.271085 
        1156         1157         1158         1159         1160 
 3344.480706  6099.668999 11689.313752  6106.758764   758.091881 
        1161         1162         1163         1164         1165 
10972.665258  9974.223174 15169.235772 15094.736542  9525.976381 
        1166         1167         1168         1169         1170 
 -301.334283 14277.362372  -598.913532  8790.715167  9070.889420 
        1171         1172         1173         1174         1175 
10984.856615  8889.461276  -682.268976 27890.235086 12399.113208 
        1176         1177         1178         1179         1180 
11549.724995  7910.798567    25.169689  7376.612221  4178.557353 
        1181         1182         1183         1184         1185 
30407.063563  3712.876911  8352.610129 11613.342667 11734.431644 
        1186         1187         1188         1189         1190 
 1096.525128  7316.897748 34248.893460  3429.934192 11919.288977 
        1191         1192         1193         1194         1195 
16879.009819 13043.713652  8805.641391 14912.388849  1959.591373 
        1196         1197         1198         1199         1200 
 3976.322196 10446.900988 13011.855046  4129.696915  5228.803620 
        1201         1202         1203         1204         1205 
 3923.781639 14104.258782 38309.250315 11599.645780 10338.542860 
        1206         1207         1208         1209         1210 
 8805.874513  9054.397148  7062.780249 11120.389238 38740.977315 
        1211         1212         1213         1214         1215 
11310.991879   667.942720 15863.710243  6992.993155  9639.580585 
        1216         1217         1218         1219         1220 
30874.500078  5091.576938  7987.077529  9205.093012 10721.330323 
        1221         1222         1223         1224         1225 
 6067.823798  -909.329016 12950.772574 15763.803247 39387.772726 
        1226         1227         1228         1229         1230 
 5807.819621 35753.275957 30238.573131 16493.551855 30446.730946 
        1231         1232         1233         1234         1235 
33322.895380 12333.179982 11717.475617 13956.803516  6845.635255 
        1236         1237         1238         1239         1240 
12699.431158 12751.312341  5526.117411  8196.777154  8724.269664 
        1241         1242         1243         1244         1245 
 8932.417809  3845.407358 10953.420286  8978.074783 13100.449364 
        1246         1247         1248         1249         1250 
  113.430652 16452.956351 12671.156751 29844.913745 13466.160154 
        1251         1252         1253         1254         1255 
 7243.980074  4417.414498 28797.369719 34979.408285  4489.454284 
        1256         1257         1258         1259         1260 
  954.443911 12304.818918 10890.544566  3731.420763 34355.222606 
        1261         1262         1263         1264         1265 
29328.627017 35061.621422 39273.412429 10017.887468  6828.094444 
        1266         1267         1268         1269         1270 
26814.031612 10633.501193  5107.063019 13045.597774 11190.117653 
        1271         1272         1273         1274         1275 
 3782.009631 23943.380109 12375.279613 11399.590326 10529.546403 
        1276         1277         1278         1279         1280 
27714.383685 15043.660368  8354.191677 33322.950230  8099.172782 
        1281         1282         1283         1284         1285 
15103.562121 40022.157839 32801.932911 33400.515171 27059.466996 
        1286         1287         1288         1289         1290 
 1909.258331  1476.556032 30918.146986  9718.591217 32998.506889 
        1291         1292         1293         1294         1295 
 6519.256531  4766.941173  4908.665022  3802.841259  7337.504525 
        1296         1297         1298         1299         1300 
11293.324958  9210.256364 31474.714380  9750.585062  8414.181847 
        1301         1302         1303         1304         1305 
31778.594798 11073.167811 14944.780632 30101.487458  4528.369023 
        1306         1307         1308         1309         1310 
12385.759135   683.846486 29613.840252 14214.316694 11136.242635 
        1311         1312         1313         1314         1315 
 2539.737186 15089.963564 17483.584416  5293.162042  9545.311182 
        1316         1317         1318         1319         1320 
10768.410977 37570.377275 12947.220063 16275.093359 12616.696785 
        1321         1322         1323         1324         1325 
12615.534967  8657.779418  8102.304478 11045.935379  4007.768339 
        1326         1327         1328         1329         1330 
 4585.249117 26485.358111 11251.577994  6250.490911 12283.617948 
        1331         1332         1333         1334         1335 
27703.440151  8657.764231 32538.025549 11479.345192 32029.516831 
        1336         1337         1338 
 7201.641940  3894.686926 33738.686771

# return a data frame
augment(mdl2)

# A tibble: 1,338 x 13
    costs body_mass smoker age_yrs no_children  noise .fitted .se.fit
    <dbl>     <dbl> <chr>    <dbl>       <dbl>  <dbl>   <dbl>   <dbl>
 1 38793.      42.2 yes         18           0  1.58   30345.    641.
 2  8311.      30.7 no          43           2 -0.599   9657.    251.
 3 12979.      37.4 no          62           0 -0.416  15822.    402.
 4 10157.      23.2 no          49           2 -0.187   8880.    334.
 5  8733.      40.4 no          46           2 -0.876  13493.    378.
 6 13982.      36.8 no          63           0 -1.86   15525.    509.
 7  8538.      33.2 no          41           3  0.183  10603.    330.
 8 12269.      32.8 no          55           2  0.499  13693.    301.
 9  9635.      37.4 no          52           0  2.29   13902.    516.
10  2138.      25.7 no          25           0  0.275   2685.    314.
# … with 1,328 more rows, and 5 more variables: .resid <dbl>, .hat <dbl>,
#   .sigma <dbl>, .cooksd <dbl>, .std.resid <dbl>

library(tidyverse)
library(dbplyr)


Attaching package: 'dbplyr'

The following objects are masked from 'package:dplyr':

    ident, sql

library(mlbench)
#mdl%>% augment()%>%arange(desc(.hat))%>% 
#  head()

dim(healthcare)

[1] 1338    8

Problem 2

Use the National Health and Nutrition Examination Survey dataset nhanes (see below) for this problem.

Use the nhanes data to predict the outcome DIQ010 indicating diabetes diagnosis (yes/no) from the above dataset.
Prepare your dataset (e.g., to avoid overfitting)
Fit you logistic regression, random forest, and gbm models to predict DIQ010
Tune your models to optimize performance
Show and explain your results, use plots where appropriate
Evaluate comparative model performance
State your conclusions

#  Do not change the code in this chunk!
nhanes <- read_csv('nhanes.csv')

Diabetes data set

library(mlbench)
data("nhanes")

Warning in data("nhanes"): data set 'nhanes' not found

glimpse(nhanes)

Observations: 26,193
Variables: 36
$ INDFMPIR <dbl> 4.65, 5.00, 5.00, 5.00, 0.46, 1.06, 1.22, 3.03, 1.76, 1…
$ RIAGENDR <chr> "Female", "Male", "Female", "Male", "Male", "Female", "…
$ RIDAGEYR <dbl> 44, 70, 16, 19, 21, 16, 79, 59, 27, 44, 62, 38, 43, 71,…
$ RIDRETH1 <chr> "Non-Hispanic Black", "Non-Hispanic White", "Non-Hispan…
$ DR1_300  <chr> "Much less than usual", "Usual", "Much less than usual"…
$ DR1_320Z <dbl> 192.56, 829.50, 118.50, 1539.20, 2577.38, 0.00, 2281.13…
$ DR1TALCO <dbl> 0.0, 40.8, 0.0, 0.0, 36.3, 0.0, 54.3, 0.0, 0.0, 0.0, 30…
$ DR1TCAFF <dbl> 13, 260, 71, 0, 10, 121, 95, 249, 39, 218, 203, 132, 3,…
$ DR1TCARB <dbl> 233.73, 269.93, 238.62, 243.56, 243.38, 275.62, 294.99,…
$ DR1TCHOL <dbl> 48, 138, 132, 359, 80, 189, 98, 79, 1103, 36, 139, 517,…
$ DR1TFIBE <dbl> 6.4, 20.3, 8.3, 14.3, 10.2, 9.7, 30.3, 8.7, 15.2, 66.0,…
$ DR1TKCAL <dbl> 1458, 2168, 1688, 2232, 2083, 2322, 2134, 1722, 2223, 3…
$ DR1TPROT <dbl> 27.43, 75.81, 45.92, 95.17, 51.05, 84.28, 73.87, 40.29,…
$ DR1TSFAT <dbl> 18.274, 17.608, 18.362, 47.397, 21.908, 38.860, 8.661, …
$ DR1TSODI <dbl> 1426, 3708, 1937, 3289, 2959, 3090, 2031, 2006, 4155, 3…
$ DR1TSUGR <dbl> 146.01, 111.54, 136.71, 92.63, 77.70, 152.66, 133.37, 1…
$ DR1TTFAT <dbl> 50.86, 60.16, 63.84, 100.19, 74.98, 101.08, 39.96, 51.2…
$ BMXBMI   <dbl> 30.90, 24.74, 16.79, 22.57, 25.03, 18.28, 28.93, 29.51,…
$ BPXDI1   <dbl> 74, 60, 58, 62, 74, 42, 74, 76, 62, 82, 80, 62, 92, 74,…
$ BPXPLS   <dbl> 58, 62, 88, 68, 54, 70, 66, 56, 78, 74, 62, 62, 80, 54,…
$ BPXSY1   <dbl> 144, 138, 120, 108, 116, 106, 144, 136, 94, 120, 154, 1…
$ LBDSBUSI <dbl> 2.14, 8.93, 2.50, 4.28, 3.21, 3.93, 3.57, 5.71, 2.14, 6…
$ LBDSCHSI <dbl> 2.664, 3.931, 3.853, 4.241, 4.267, 3.258, 4.836, 5.275,…
$ LBDSCRSI <dbl> 70.72, 106.08, 79.56, 70.72, 61.88, 61.88, 79.56, 79.56…
$ LBDSGLSI <dbl> 4.83, 8.60, 4.39, 4.22, 4.50, 4.83, 5.22, 4.55, 4.00, 4…
$ LBDSTPSI <dbl> 69, 72, 78, 72, 73, 72, 75, 69, 64, 68, 72, 72, 76, 66,…
$ LBDSTRSI <dbl> 0.881, 0.666, 0.553, 1.118, 0.294, 0.632, 0.508, 1.242,…
$ LBDTCSI  <dbl> 2.72, 3.80, 3.80, 2.79, 5.35, 3.26, 4.68, 5.30, 6.28, 5…
$ LBXGH    <dbl> 6.0, 7.1, 4.7, 4.7, 4.8, 5.0, 5.0, 5.8, 4.3, 4.6, 6.1, …
$ LBXSAPSI <dbl> 74, 48, 41, 47, 183, 104, 67, 99, 72, 75, 153, 44, 84, …
$ LBXSBU   <dbl> 6, 25, 7, 12, 9, 11, 10, 16, 6, 18, 13, 10, 13, 11, 12,…
$ LBXSNASI <dbl> 137, 140, 137, 143, 139, 139, 139, 140, 139, 138, 139, …
$ LBXSOSSI <dbl> 271, 287, 271, 283, 275, 276, 276, 280, 274, 277, 277, …
$ DIQ010   <chr> "No", "Yes", "No", "No", "No", "No", "No", "Yes", "No",…
$ SLQ050   <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No", …
$ WHQ030   <chr> "Overweight,", "Overweight,", "Underweight, or", "About…

nhanes <- read_csv('nhanes.csv')

Parsed with column specification:
cols(
  .default = col_double(),
  RIAGENDR = col_character(),
  RIDRETH1 = col_character(),
  DR1_300 = col_character(),
  DIQ010 = col_character(),
  SLQ050 = col_character(),
  WHQ030 = col_character()
)

See spec(...) for full column specifications.

nhanes$DIQ010 <- ifelse(nhanes$DIQ010=='Yes', 1,0)
nhanes

# A tibble: 26,193 x 36
   INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
      <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
 1     4.65 Female         44 Non-His… Much l…     193.      0         13
 2     5    Male           70 Non-His… Usual       830.     40.8      260
 3     5    Female         16 Non-His… Much l…     118.      0         71
 4     5    Male           19 Non-His… Usual      1539.      0          0
 5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
 6     1.06 Female         16 Non-His… Usual         0       0        121
 7     1.22 Male           79 Non-His… Usual      2281.     54.3       95
 8     3.03 Female         59 Non-His… Much l…     974       0        249
 9     1.76 Female         27 Mexican… Usual       622.      0         39
10     1.03 Female         44 Other R… Usual      1421.      0        218
# … with 26,183 more rows, and 28 more variables: DR1TCARB <dbl>,
#   DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>,
#   DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>,
#   BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>,
#   LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>,
#   LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>,
#   LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>,
#   DIQ010 <dbl>, SLQ050 <chr>, WHQ030 <chr>

nhanesmodel <- glm(DIQ010~., data=nhanes, family ='binomial')

summary(nhanesmodel)


Call:
glm(formula = DIQ010 ~ ., family = "binomial", data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.2233  -0.3367  -0.1947  -0.1136   4.0299  

Coefficients:
                                              Estimate Std. Error z value
(Intercept)                                 -1.603e+01  1.811e+00  -8.852
INDFMPIR                                    -5.140e-02  1.731e-02  -2.970
RIAGENDRMale                                 4.960e-03  6.023e-02   0.082
RIDAGEYR                                     3.652e-02  2.114e-03  17.277
RIDRETH1Non-Hispanic Black                   1.288e-01  8.961e-02   1.437
RIDRETH1Non-Hispanic White                  -2.463e-01  8.338e-02  -2.954
RIDRETH1Other Hispanic                       2.465e-02  1.059e-01   0.233
RIDRETH1Other Race - Including Multi-Racial -3.790e-02  1.143e-01  -0.332
DR1_300Much more than usual                  8.695e-02  1.074e-01   0.809
DR1_300Usual                                 3.260e-02  6.906e-02   0.472
DR1_320Z                                     1.024e-05  2.356e-05   0.435
DR1TALCO                                     1.266e-02  1.065e-02   1.188
DR1TCAFF                                     4.228e-04  1.225e-04   3.451
DR1TCARB                                     7.869e-03  6.367e-03   1.236
DR1TCHOL                                     1.678e-04  1.527e-04   1.099
DR1TFIBE                                     9.775e-03  4.853e-03   2.014
DR1TKCAL                                    -2.290e-03  1.536e-03  -1.490
DR1TPROT                                     5.844e-03  6.537e-03   0.894
DR1TSFAT                                    -9.169e-04  4.350e-03  -0.211
DR1TSODI                                     9.272e-05  2.848e-05   3.255
DR1TSUGR                                    -4.702e-03  9.907e-04  -4.746
DR1TTFAT                                     2.196e-02  1.338e-02   1.641
BMXBMI                                       4.021e-02  4.280e-03   9.394
BPXDI1                                      -5.066e-03  2.129e-03  -2.379
BPXPLS                                       4.583e-03  2.256e-03   2.031
BPXSY1                                       2.554e-03  1.576e-03   1.621
LBDSBUSI                                    -1.335e+01  9.003e+00  -1.483
LBDSCHSI                                    -3.444e-01  1.419e-01  -2.427
LBDSCRSI                                     2.345e-03  6.783e-04   3.457
LBDSGLSI                                     9.448e-02  5.519e-02   1.712
LBDSTPSI                                     2.476e-03  5.809e-03   0.426
LBDSTRSI                                     9.993e-02  2.196e-02   4.550
LBDTCSI                                     -1.270e-01  1.446e-01  -0.878
LBXGH                                        1.306e+00  4.252e-02  30.718
LBXSAPSI                                    -3.381e-03  1.109e-03  -3.049
LBXSBU                                       4.783e+00  3.214e+00   1.488
LBXSNASI                                     1.288e-02  9.791e-02   0.132
LBXSOSSI                                     8.642e-03  5.194e-02   0.166
SLQ050Yes                                    5.736e-01  5.550e-02  10.335
WHQ030Overweight,                            2.316e-01  6.783e-02   3.415
WHQ030Underweight, or                        1.147e-01  1.477e-01   0.777
                                            Pr(>|z|)    
(Intercept)                                  < 2e-16 ***
INDFMPIR                                    0.002976 ** 
RIAGENDRMale                                0.934366    
RIDAGEYR                                     < 2e-16 ***
RIDRETH1Non-Hispanic Black                  0.150709    
RIDRETH1Non-Hispanic White                  0.003132 ** 
RIDRETH1Other Hispanic                      0.815940    
RIDRETH1Other Race - Including Multi-Racial 0.740169    
DR1_300Much more than usual                 0.418287    
DR1_300Usual                                0.636910    
DR1_320Z                                    0.663761    
DR1TALCO                                    0.234663    
DR1TCAFF                                    0.000559 ***
DR1TCARB                                    0.216486    
DR1TCHOL                                    0.271842    
DR1TFIBE                                    0.043984 *  
DR1TKCAL                                    0.136155    
DR1TPROT                                    0.371330    
DR1TSFAT                                    0.833072    
DR1TSODI                                    0.001133 ** 
DR1TSUGR                                    2.07e-06 ***
DR1TTFAT                                    0.100868    
BMXBMI                                       < 2e-16 ***
BPXDI1                                      0.017339 *  
BPXPLS                                      0.042230 *  
BPXSY1                                      0.105036    
LBDSBUSI                                    0.138128    
LBDSCHSI                                    0.015232 *  
LBDSCRSI                                    0.000546 ***
LBDSGLSI                                    0.086907 .  
LBDSTPSI                                    0.669937    
LBDSTRSI                                    5.36e-06 ***
LBDTCSI                                     0.380017    
LBXGH                                        < 2e-16 ***
LBXSAPSI                                    0.002297 ** 
LBXSBU                                      0.136689    
LBXSNASI                                    0.895328    
LBXSOSSI                                    0.867862    
SLQ050Yes                                    < 2e-16 ***
WHQ030Overweight,                           0.000639 ***
WHQ030Underweight, or                       0.437320    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 10584  on 26152  degrees of freedom
AIC: 10666

Number of Fisher Scoring iterations: 6

augment(nhanesmodel)

# A tibble: 26,193 x 43
   DIQ010 INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO
    <dbl>    <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>
 1      0     4.65 Female         44 Non-His… Much l…     193.      0  
 2      1     5    Male           70 Non-His… Usual       830.     40.8
 3      0     5    Female         16 Non-His… Much l…     118.      0  
 4      0     5    Male           19 Non-His… Usual      1539.      0  
 5      0     0.46 Male           21 Other H… Much l…    2577.     36.3
 6      0     1.06 Female         16 Non-His… Usual         0       0  
 7      0     1.22 Male           79 Non-His… Usual      2281.     54.3
 8      1     3.03 Female         59 Non-His… Much l…     974       0  
 9      0     1.76 Female         27 Mexican… Usual       622.      0  
10      0     1.03 Female         44 Other R… Usual      1421.      0  
# … with 26,183 more rows, and 35 more variables: DR1TCAFF <dbl>,
#   DR1TCARB <dbl>, DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>,
#   DR1TPROT <dbl>, DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>,
#   DR1TTFAT <dbl>, BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>,
#   BPXSY1 <dbl>, LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSGLSI <dbl>, LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>,
#   LBXGH <dbl>, LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>,
#   LBXSOSSI <dbl>, SLQ050 <chr>, WHQ030 <chr>, .fitted <dbl>,
#   .se.fit <dbl>, .resid <dbl>, .hat <dbl>, .sigma <dbl>, .cooksd <dbl>,
#   .std.resid <dbl>

augment(nhanesmodel,type.predict="response")

# A tibble: 26,193 x 43
   DIQ010 INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO
    <dbl>    <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>
 1      0     4.65 Female         44 Non-His… Much l…     193.      0  
 2      1     5    Male           70 Non-His… Usual       830.     40.8
 3      0     5    Female         16 Non-His… Much l…     118.      0  
 4      0     5    Male           19 Non-His… Usual      1539.      0  
 5      0     0.46 Male           21 Other H… Much l…    2577.     36.3
 6      0     1.06 Female         16 Non-His… Usual         0       0  
 7      0     1.22 Male           79 Non-His… Usual      2281.     54.3
 8      1     3.03 Female         59 Non-His… Much l…     974       0  
 9      0     1.76 Female         27 Mexican… Usual       622.      0  
10      0     1.03 Female         44 Other R… Usual      1421.      0  
# … with 26,183 more rows, and 35 more variables: DR1TCAFF <dbl>,
#   DR1TCARB <dbl>, DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>,
#   DR1TPROT <dbl>, DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>,
#   DR1TTFAT <dbl>, BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>,
#   BPXSY1 <dbl>, LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSGLSI <dbl>, LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>,
#   LBXGH <dbl>, LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>,
#   LBXSOSSI <dbl>, SLQ050 <chr>, WHQ030 <chr>, .fitted <dbl>,
#   .se.fit <dbl>, .resid <dbl>, .hat <dbl>, .sigma <dbl>, .cooksd <dbl>,
#   .std.resid <dbl>

Logistic regression problem first try at it.
Changed the DIQ010 value from yes/no to O and 1
Looked at the data set and wrote a logistic regression model and ran a prediction on it.
Star values are the significant low pvalues.
look at .fitted, .se.fit, .resid, .hat, .sigma, .cooksd, .std.resid

augment shows fitted values on log odd scale not useful set type.predict = response retrial familar probablity scale probablility of diabetes is limited make prediction not in our data set need out of sample predictions need to use new data to augment.

# create new data frame
new_data <- data.frame(LBXGH = 5.0)

# make predictions
augment(nhanesmodel, newdata = new_data, type.predict = "response")

# A tibble: 26,193 x 2
   LBXGH .fitted
   <dbl>   <dbl>
 1     5 0.112  
 2     5 0.607  
 3     5 0.00309
 4     5 0.00428
 5     5 0.00286
 6     5 0.00450
 7     5 0.0360 
 8     5 0.0916 
 9     5 0.00355
10     5 0.0283 
# … with 26,183 more rows

exp(coef(nhanesmodel ))

                                (Intercept) 
                               1.091207e-07 
                                   INDFMPIR 
                               9.498951e-01 
                               RIAGENDRMale 
                               1.004972e+00 
                                   RIDAGEYR 
                               1.037198e+00 
                 RIDRETH1Non-Hispanic Black 
                               1.137436e+00 
                 RIDRETH1Non-Hispanic White 
                               7.816613e-01 
                     RIDRETH1Other Hispanic 
                               1.024959e+00 
RIDRETH1Other Race - Including Multi-Racial 
                               9.628107e-01 
                DR1_300Much more than usual 
                               1.090846e+00 
                               DR1_300Usual 
                               1.033133e+00 
                                   DR1_320Z 
                               1.000010e+00 
                                   DR1TALCO 
                               1.012741e+00 
                                   DR1TCAFF 
                               1.000423e+00 
                                   DR1TCARB 
                               1.007900e+00 
                                   DR1TCHOL 
                               1.000168e+00 
                                   DR1TFIBE 
                               1.009823e+00 
                                   DR1TKCAL 
                               9.977130e-01 
                                   DR1TPROT 
                               1.005861e+00 
                                   DR1TSFAT 
                               9.990835e-01 
                                   DR1TSODI 
                               1.000093e+00 
                                   DR1TSUGR 
                               9.953088e-01 
                                   DR1TTFAT 
                               1.022202e+00 
                                     BMXBMI 
                               1.041026e+00 
                                     BPXDI1 
                               9.949473e-01 
                                     BPXPLS 
                               1.004594e+00 
                                     BPXSY1 
                               1.002557e+00 
                                   LBDSBUSI 
                               1.594505e-06 
                                   LBDSCHSI 
                               7.086385e-01 
                                   LBDSCRSI 
                               1.002347e+00 
                                   LBDSGLSI 
                               1.099082e+00 
                                   LBDSTPSI 
                               1.002479e+00 
                                   LBDSTRSI 
                               1.105096e+00 
                                    LBDTCSI 
                               8.807696e-01 
                                      LBXGH 
                               3.691852e+00 
                                   LBXSAPSI 
                               9.966245e-01 
                                     LBXSBU 
                               1.194472e+02 
                                   LBXSNASI 
                               1.012965e+00 
                                   LBXSOSSI 
                               1.008679e+00 
                                  SLQ050Yes 
                               1.774707e+00 
                          WHQ030Overweight, 
                               1.260621e+00 
                      WHQ030Underweight, or 
                               1.121561e+00

Patient who drink high amounts of alcohol, caffeine, carbs, cholesterol, protein, sodium, sugar, fats, have high BMI, 60 sec pulse , systolic, creatinine, glucose serum, total protein, triglycerides, cholesterol, glycohemoglobin, sodium,osmolality, SLQ050,over and under weight

# data frame with binary predictions
tidy_mod <- augment(nhanesmodel, type.predict = "response") %>% 
  mutate(DIQ010_hat = round(.fitted)) 
  
# confusion matrix
tidy_mod %>% 
  select(DIQ010, DIQ010_hat) %>%
  table()

      DIQ010_hat
DIQ010     0     1
     0 22637   373
     1  1517  1666

With the confusion matrix we see 226636 was true negatives and 373 false positives 1517 false negative and 1666 was true positive

library(broom)
# Use broom::augment to augment the model  
aug_nhanesmodel <- augment(nhanesmodel) 
glimpse(aug_nhanesmodel)

Observations: 26,193
Variables: 43
$ DIQ010     <dbl> 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,…
$ INDFMPIR   <dbl> 4.65, 5.00, 5.00, 5.00, 0.46, 1.06, 1.22, 3.03, 1.76,…
$ RIAGENDR   <chr> "Female", "Male", "Female", "Male", "Male", "Female",…
$ RIDAGEYR   <dbl> 44, 70, 16, 19, 21, 16, 79, 59, 27, 44, 62, 38, 43, 7…
$ RIDRETH1   <chr> "Non-Hispanic Black", "Non-Hispanic White", "Non-Hisp…
$ DR1_300    <chr> "Much less than usual", "Usual", "Much less than usua…
$ DR1_320Z   <dbl> 192.56, 829.50, 118.50, 1539.20, 2577.38, 0.00, 2281.…
$ DR1TALCO   <dbl> 0.0, 40.8, 0.0, 0.0, 36.3, 0.0, 54.3, 0.0, 0.0, 0.0, …
$ DR1TCAFF   <dbl> 13, 260, 71, 0, 10, 121, 95, 249, 39, 218, 203, 132, …
$ DR1TCARB   <dbl> 233.73, 269.93, 238.62, 243.56, 243.38, 275.62, 294.9…
$ DR1TCHOL   <dbl> 48, 138, 132, 359, 80, 189, 98, 79, 1103, 36, 139, 51…
$ DR1TFIBE   <dbl> 6.4, 20.3, 8.3, 14.3, 10.2, 9.7, 30.3, 8.7, 15.2, 66.…
$ DR1TKCAL   <dbl> 1458, 2168, 1688, 2232, 2083, 2322, 2134, 1722, 2223,…
$ DR1TPROT   <dbl> 27.43, 75.81, 45.92, 95.17, 51.05, 84.28, 73.87, 40.2…
$ DR1TSFAT   <dbl> 18.274, 17.608, 18.362, 47.397, 21.908, 38.860, 8.661…
$ DR1TSODI   <dbl> 1426, 3708, 1937, 3289, 2959, 3090, 2031, 2006, 4155,…
$ DR1TSUGR   <dbl> 146.01, 111.54, 136.71, 92.63, 77.70, 152.66, 133.37,…
$ DR1TTFAT   <dbl> 50.86, 60.16, 63.84, 100.19, 74.98, 101.08, 39.96, 51…
$ BMXBMI     <dbl> 30.90, 24.74, 16.79, 22.57, 25.03, 18.28, 28.93, 29.5…
$ BPXDI1     <dbl> 74, 60, 58, 62, 74, 42, 74, 76, 62, 82, 80, 62, 92, 7…
$ BPXPLS     <dbl> 58, 62, 88, 68, 54, 70, 66, 56, 78, 74, 62, 62, 80, 5…
$ BPXSY1     <dbl> 144, 138, 120, 108, 116, 106, 144, 136, 94, 120, 154,…
$ LBDSBUSI   <dbl> 2.14, 8.93, 2.50, 4.28, 3.21, 3.93, 3.57, 5.71, 2.14,…
$ LBDSCHSI   <dbl> 2.664, 3.931, 3.853, 4.241, 4.267, 3.258, 4.836, 5.27…
$ LBDSCRSI   <dbl> 70.72, 106.08, 79.56, 70.72, 61.88, 61.88, 79.56, 79.…
$ LBDSGLSI   <dbl> 4.83, 8.60, 4.39, 4.22, 4.50, 4.83, 5.22, 4.55, 4.00,…
$ LBDSTPSI   <dbl> 69, 72, 78, 72, 73, 72, 75, 69, 64, 68, 72, 72, 76, 6…
$ LBDSTRSI   <dbl> 0.881, 0.666, 0.553, 1.118, 0.294, 0.632, 0.508, 1.24…
$ LBDTCSI    <dbl> 2.72, 3.80, 3.80, 2.79, 5.35, 3.26, 4.68, 5.30, 6.28,…
$ LBXGH      <dbl> 6.0, 7.1, 4.7, 4.7, 4.8, 5.0, 5.0, 5.8, 4.3, 4.6, 6.1…
$ LBXSAPSI   <dbl> 74, 48, 41, 47, 183, 104, 67, 99, 72, 75, 153, 44, 84…
$ LBXSBU     <dbl> 6, 25, 7, 12, 9, 11, 10, 16, 6, 18, 13, 10, 13, 11, 1…
$ LBXSNASI   <dbl> 137, 140, 137, 143, 139, 139, 139, 140, 139, 138, 139…
$ LBXSOSSI   <dbl> 271, 287, 271, 283, 275, 276, 276, 280, 274, 277, 277…
$ SLQ050     <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No"…
$ WHQ030     <chr> "Overweight,", "Overweight,", "Underweight, or", "Abo…
$ .fitted    <dbl> -2.0740109, 0.4336325, -5.7762650, -5.4491232, -5.854…
$ .se.fit    <dbl> 0.1427966, 0.1303179, 0.2028511, 0.2515243, 0.2686952…
$ .resid     <dbl> -0.48659613, 0.99965363, -0.07868262, -0.09263751, -0…
$ .hat       <dbl> 2.022924e-03, 4.052159e-03, 1.269036e-04, 2.699478e-0…
$ .sigma     <dbl> 0.6361871, 0.6361640, 0.6361940, 0.6361939, 0.6361940…
$ .cooksd    <dbl> 6.226199e-06, 6.458106e-05, 9.598435e-09, 2.832738e-0…
$ .std.resid <dbl> -0.48708905, 1.00168519, -0.07868762, -0.09265002, -0…

The augment() function from the broom package does exactly this. It takes a model object as an argument and returns a data frame that contains the data on which the model was fit, along with several quantities specific to the regression model, including the fitted values, residuals, leverage scores, and standardized residuals.

RMSE if it is spread out data Higher rmse poor model fit prediction Lower rmse closer strong fitted and acual value

# scatterplot with jitter
data_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = LBXGH)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# linear regression line for the scatter plot
data_nhanes + 
  geom_smooth(method = "lm", se = FALSE)

#checking high LBXGH values above 6.5
glycohemoglobin <- nhanes %>%
  filter( LBXGH >= 6.5, LBXGH <= 10)

# scatterplot with jitter
data_glycohemoglobin <- ggplot(data = glycohemoglobin, aes(y = DIQ010, x = LBXGH)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# linear regression line
data_glycohemoglobin + 
 geom_smooth(method = "lm", se = FALSE)

#check with lower LBXGH values
lowglycohemoglobin <- nhanes %>%
  filter( LBXGH >= 4, LBXGH <= 6.5)

# scatterplot with jitter
low_glycohemoglobin <- ggplot(data = lowglycohemoglobin , aes(y = DIQ010, x = LBXGH)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# linear regression line
low_glycohemoglobin + 
 geom_smooth(method = "lm", se = FALSE)

# fit model
Glycohemoglobin_model <- glm(DIQ010 ~ LBXGH, data = nhanes, family = binomial)
summary(Glycohemoglobin_model)


Call:
glm(formula = DIQ010 ~ LBXGH, family = binomial, data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-5.1050  -0.3836  -0.2897  -0.2180   3.6383  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -13.35947    0.20687  -64.58   <2e-16 ***
LBXGH         1.92629    0.03456   55.74   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 12358  on 26191  degrees of freedom
AIC: 12362

Number of Fisher Scoring iterations: 6

glimpse(Glycohemoglobin_model)

List of 30
 $ coefficients     : Named num [1:2] -13.36 1.93
  ..- attr(*, "names")= chr [1:2] "(Intercept)" "LBXGH"
 $ residuals        : Named num [1:26193] -1.17 1.73 -1.01 -1.01 -1.02 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ fitted.values    : Named num [1:26193] 0.1416 0.5786 0.0133 0.0133 0.0161 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ effects          : Named num [1:26193] 78.358 -55.737 -0.111 -0.111 -0.122 ...
  ..- attr(*, "names")= chr [1:26193] "(Intercept)" "LBXGH" "" "" ...
 $ R                : num [1:2, 1:2] -41 0 -244 -28.9
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:2] "(Intercept)" "LBXGH"
  .. ..$ : chr [1:2] "(Intercept)" "LBXGH"
 $ rank             : int 2
 $ qr               :List of 5
  ..$ qr   : num [1:26193, 1:2] -41.0406 0.01203 0.00279 0.00279 0.00307 ...
  .. ..- attr(*, "dimnames")=List of 2
  ..$ rank : int 2
  ..$ qraux: num [1:2] 1.01 1.02
  ..$ pivot: int [1:2] 1 2
  ..$ tol  : num 1e-11
  ..- attr(*, "class")= chr "qr"
 $ family           :List of 12
  ..$ family    : chr "binomial"
  ..$ link      : chr "logit"
  ..$ linkfun   :function (mu)  
  ..$ linkinv   :function (eta)  
  ..$ variance  :function (mu)  
  ..$ dev.resids:function (y, mu, wt)  
  ..$ aic       :function (y, n, mu, wt, dev)  
  ..$ mu.eta    :function (eta)  
  ..$ initialize:  expression({  if (NCOL(y) == 1) {  if (is.factor(y))  y <- y != levels(y)[1L]  n <- rep.int(1, nobs)  y[weights =| __truncated__
  ..$ validmu   :function (mu)  
  ..$ valideta  :function (eta)  
  ..$ simulate  :function (object, nsim)  
  ..- attr(*, "class")= chr "family"
 $ linear.predictors: Named num [1:26193] -1.802 0.317 -4.306 -4.306 -4.113 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ deviance         : num 12358
 $ aic              : num 12362
 $ null.deviance    : num 19380
 $ iter             : int 6
 $ weights          : Named num [1:26193] 0.1216 0.2438 0.0131 0.0131 0.0158 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ prior.weights    : Named num [1:26193] 1 1 1 1 1 1 1 1 1 1 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ df.residual      : int 26191
 $ df.null          : int 26192
 $ y                : Named num [1:26193] 0 1 0 0 0 0 0 1 0 0 ...
  ..- attr(*, "names")= chr [1:26193] "1" "2" "3" "4" ...
 $ converged        : logi TRUE
 $ boundary         : logi FALSE
 $ model            :'data.frame':  26193 obs. of  2 variables:
  ..$ DIQ010: num [1:26193] 0 1 0 0 0 0 0 1 0 0 ...
  ..$ LBXGH : num [1:26193] 6 7.1 4.7 4.7 4.8 5 5 5.8 4.3 4.6 ...
  ..- attr(*, "terms")=Classes 'terms', 'formula'  language DIQ010 ~ LBXGH
  .. .. ..- attr(*, "variables")= language list(DIQ010, LBXGH)
  .. .. ..- attr(*, "factors")= int [1:2, 1] 0 1
  .. .. .. ..- attr(*, "dimnames")=List of 2
  .. .. ..- attr(*, "term.labels")= chr "LBXGH"
  .. .. ..- attr(*, "order")= int 1
  .. .. ..- attr(*, "intercept")= int 1
  .. .. ..- attr(*, "response")= int 1
  .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
  .. .. ..- attr(*, "predvars")= language list(DIQ010, LBXGH)
  .. .. ..- attr(*, "dataClasses")= Named chr [1:2] "numeric" "numeric"
  .. .. .. ..- attr(*, "names")= chr [1:2] "DIQ010" "LBXGH"
 $ call             : language glm(formula = DIQ010 ~ LBXGH, family = binomial, data = nhanes)
 $ formula          :Class 'formula'  language DIQ010 ~ LBXGH
  .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
 $ terms            :Classes 'terms', 'formula'  language DIQ010 ~ LBXGH
  .. ..- attr(*, "variables")= language list(DIQ010, LBXGH)
  .. ..- attr(*, "factors")= int [1:2, 1] 0 1
  .. .. ..- attr(*, "dimnames")=List of 2
  .. ..- attr(*, "term.labels")= chr "LBXGH"
  .. ..- attr(*, "order")= int 1
  .. ..- attr(*, "intercept")= int 1
  .. ..- attr(*, "response")= int 1
  .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
  .. ..- attr(*, "predvars")= language list(DIQ010, LBXGH)
  .. ..- attr(*, "dataClasses")= Named chr [1:2] "numeric" "numeric"
  .. .. ..- attr(*, "names")= chr [1:2] "DIQ010" "LBXGH"
 $ data             :Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame':   26193 obs. of  36 variables:
  ..$ INDFMPIR: num [1:26193] 4.65 5 5 5 0.46 1.06 1.22 3.03 1.76 1.03 ...
  ..$ RIAGENDR: chr [1:26193] "Female" "Male" "Female" "Male" ...
  ..$ RIDAGEYR: num [1:26193] 44 70 16 19 21 16 79 59 27 44 ...
  ..$ RIDRETH1: chr [1:26193] "Non-Hispanic Black" "Non-Hispanic White" "Non-Hispanic Black" "Non-Hispanic White" ...
  ..$ DR1_300 : chr [1:26193] "Much less than usual" "Usual" "Much less than usual" "Usual" ...
  ..$ DR1_320Z: num [1:26193] 193 830 118 1539 2577 ...
  ..$ DR1TALCO: num [1:26193] 0 40.8 0 0 36.3 0 54.3 0 0 0 ...
  ..$ DR1TCAFF: num [1:26193] 13 260 71 0 10 121 95 249 39 218 ...
  ..$ DR1TCARB: num [1:26193] 234 270 239 244 243 ...
  ..$ DR1TCHOL: num [1:26193] 48 138 132 359 80 ...
  ..$ DR1TFIBE: num [1:26193] 6.4 20.3 8.3 14.3 10.2 9.7 30.3 8.7 15.2 66 ...
  ..$ DR1TKCAL: num [1:26193] 1458 2168 1688 2232 2083 ...
  ..$ DR1TPROT: num [1:26193] 27.4 75.8 45.9 95.2 51 ...
  ..$ DR1TSFAT: num [1:26193] 18.3 17.6 18.4 47.4 21.9 ...
  ..$ DR1TSODI: num [1:26193] 1426 3708 1937 3289 2959 ...
  ..$ DR1TSUGR: num [1:26193] 146 111.5 136.7 92.6 77.7 ...
  ..$ DR1TTFAT: num [1:26193] 50.9 60.2 63.8 100.2 75 ...
  ..$ BMXBMI  : num [1:26193] 30.9 24.7 16.8 22.6 25 ...
  ..$ BPXDI1  : num [1:26193] 74 60 58 62 74 42 74 76 62 82 ...
  ..$ BPXPLS  : num [1:26193] 58 62 88 68 54 70 66 56 78 74 ...
  ..$ BPXSY1  : num [1:26193] 144 138 120 108 116 106 144 136 94 120 ...
  ..$ LBDSBUSI: num [1:26193] 2.14 8.93 2.5 4.28 3.21 3.93 3.57 5.71 2.14 6.43 ...
  ..$ LBDSCHSI: num [1:26193] 2.66 3.93 3.85 4.24 4.27 ...
  ..$ LBDSCRSI: num [1:26193] 70.7 106.1 79.6 70.7 61.9 ...
  ..$ LBDSGLSI: num [1:26193] 4.83 8.6 4.39 4.22 4.5 4.83 5.22 4.55 4 4.88 ...
  ..$ LBDSTPSI: num [1:26193] 69 72 78 72 73 72 75 69 64 68 ...
  ..$ LBDSTRSI: num [1:26193] 0.881 0.666 0.553 1.118 0.294 ...
  ..$ LBDTCSI : num [1:26193] 2.72 3.8 3.8 2.79 5.35 3.26 4.68 5.3 6.28 5.12 ...
  ..$ LBXGH   : num [1:26193] 6 7.1 4.7 4.7 4.8 5 5 5.8 4.3 4.6 ...
  ..$ LBXSAPSI: num [1:26193] 74 48 41 47 183 104 67 99 72 75 ...
  ..$ LBXSBU  : num [1:26193] 6 25 7 12 9 11 10 16 6 18 ...
  ..$ LBXSNASI: num [1:26193] 137 140 137 143 139 139 139 140 139 138 ...
  ..$ LBXSOSSI: num [1:26193] 271 287 271 283 275 276 276 280 274 277 ...
  ..$ DIQ010  : num [1:26193] 0 1 0 0 0 0 0 1 0 0 ...
  ..$ SLQ050  : chr [1:26193] "No" "No" "No" "No" ...
  ..$ WHQ030  : chr [1:26193] "Overweight," "Overweight," "Underweight, or" "About the right weight?" ...
  ..- attr(*, "spec")=
  .. .. cols(
  .. ..   INDFMPIR = col_double(),
  .. ..   RIAGENDR = col_character(),
  .. ..   RIDAGEYR = col_double(),
  .. ..   RIDRETH1 = col_character(),
  .. ..   DR1_300 = col_character(),
  .. ..   DR1_320Z = col_double(),
  .. ..   DR1TALCO = col_double(),
  .. ..   DR1TCAFF = col_double(),
  .. ..   DR1TCARB = col_double(),
  .. ..   DR1TCHOL = col_double(),
  .. ..   DR1TFIBE = col_double(),
  .. ..   DR1TKCAL = col_double(),
  .. ..   DR1TPROT = col_double(),
  .. ..   DR1TSFAT = col_double(),
  .. ..   DR1TSODI = col_double(),
  .. ..   DR1TSUGR = col_double(),
  .. ..   DR1TTFAT = col_double(),
  .. ..   BMXBMI = col_double(),
  .. ..   BPXDI1 = col_double(),
  .. ..   BPXPLS = col_double(),
  .. ..   BPXSY1 = col_double(),
  .. ..   LBDSBUSI = col_double(),
  .. ..   LBDSCHSI = col_double(),
  .. ..   LBDSCRSI = col_double(),
  .. ..   LBDSGLSI = col_double(),
  .. ..   LBDSTPSI = col_double(),
  .. ..   LBDSTRSI = col_double(),
  .. ..   LBDTCSI = col_double(),
  .. ..   LBXGH = col_double(),
  .. ..   LBXSAPSI = col_double(),
  .. ..   LBXSBU = col_double(),
  .. ..   LBXSNASI = col_double(),
  .. ..   LBXSOSSI = col_double(),
  .. ..   DIQ010 = col_character(),
  .. ..   SLQ050 = col_character(),
  .. ..   WHQ030 = col_character()
  .. .. )
 $ offset           : NULL
 $ control          :List of 3
  ..$ epsilon: num 1e-08
  ..$ maxit  : num 25
  ..$ trace  : logi FALSE
 $ method           : chr "glm.fit"
 $ contrasts        : NULL
 $ xlevels          : Named list()
 - attr(*, "class")= chr [1:2] "glm" "lm"

# create new data frame
new_data <- data.frame(LBXGH = 8.0)

# make predictions
augment(Glycohemoglobin_model, newdata = new_data, type.predict = "response")

# A tibble: 1 x 3
  LBXGH .fitted .se.fit
  <dbl>   <dbl>   <dbl>
1     8   0.886 0.00758

ggplot(Glycohemoglobin_model, aes(x = .fitted)) +
  geom_density(aes(color = as.factor(LBXGH)))

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

Warning: Groups with fewer than two data points have been dropped.

ggplot(Glycohemoglobin_model, aes(x = .fitted)) +
  geom_density(aes(color = as.factor(DIQ010)))

1.This is a scatterplot of DIQ010 (if you have diabetes ) vs the LBXGH = Glycohemoglobin (%) levels. 2.Glycohemoglobin values above 6.5% is when the doctor tells you are pre diabetics. 3.Second graph the Glycohemoglobin % is filtered with the linear regression line is where the glycohemoglobin % is 6.5 and above.
4. Third graph is showing patient with Glycohemoglobin % between 4-6.5. These people do not have diabetes. 5. This is the best fit model for predicting diabetes using Glycohemoglobin % results. If a patient has below 6.4 glycohemoglobin they have under 50% chance to not have diabetes and if they are above 6.4 % glycohemoglobin they will have a 50% chance to have diabetes. 6. Below is a graph that shows #5’s prediction.

# data frame with binary predictions
tidy_mod <- augment(Glycohemoglobin_model, type.predict = "response") %>% 
  mutate(DIQ010_hat = round(.fitted)) 
  
# confusion matrix
tidy_mod %>% 
  select(DIQ010, DIQ010_hat) %>%
  table()

      DIQ010_hat
DIQ010     0     1
     0 22762   248
     1  1790  1393

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = LBXGH)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

1. Here is the logistic regression graph for the DIQ010 vs LBXGH variables for the nhanes dataset. Here the logistic regression line fits very nicely on the data. 2. Logistic regression is a type of Generalized Linear Model which is suitable for problems that predict a binary outcome (e.g., 1/0 or positive/negative), a classification model 3. We don’t use the linear regression because the probabilities are always between 0 and 1; OLSR models can generate outcomes that are constrained to values between 0 and 1. 4. A logistic function or logistic curve is a common “S” shape (sigmoid curve), with equation: 5. where e = the natural logarithm base Xo= the x-value of the sigmoid’s midpoint, L is the curve’s maximum value, in this case, L = 1 k = the steepness of the curve

# binned points and line
data_space <- ggplot(data = nhanes, aes(x = LBXGH, y = DIQ010)) + 
  geom_point() + geom_line()

# augmented model
MedGPA_plus <- nhanesmodel %>%
  augment(type.predict = "response")

# logistic model on probability scale
data_space +
  geom_line(data = MedGPA_plus, aes(x = DIQ010, y = .fitted), color = "red")

# compute odds for bins
# compute odds for bins
nhanes <- nhanes%>%
  mutate(odds = LBXGH / (1 - LBXGH))

# plot binned odds
data_space <- ggplot(data = nhanes, aes(x = LBXGH, y = DIQ010)) + 
  geom_point() + geom_line()

# compute odds for observations
MedGPA_plus <- MedGPA_plus %>%
  mutate(odds_hat = .fitted / (1 - .fitted))

# logistic model on odds scale
data_space +
  geom_line(data = MedGPA_plus, aes(x = LBXGH, y = DIQ010), color = "red")

# compute log odds for bins
nhanes <- nhanes %>%
  mutate(log_odds = log(LBXGH / (1 - LBXGH)))

Warning in log(LBXGH/(1 - LBXGH)): NaNs produced

# plot binned log odds
data_space <- ggplot(data =nhanes, aes(x = LBXGH, y = DIQ010)) + 
  geom_point() + geom_line()

# compute log odds for observations
MedGPA_plus <- MedGPA_plus %>%
  mutate(log_DIQ010 = log(.fitted / (1 - .fitted)))

# logistic model on log odds scale
data_space +
  geom_line(data = MedGPA_plus, aes(x = LBXGH, y = log_DIQ010), color = "red")

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = DR1TSUGR)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = BMXBMI)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = LBDSGLSI)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

Glucoseserum_model <- glm(DIQ010 ~ LBDSGLSI, data = nhanes, family = binomial)
summary(Glucoseserum_model)


Call:
glm(formula = DIQ010 ~ LBDSGLSI, family = binomial, data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-5.3870  -0.4177  -0.3535  -0.3048   3.2852  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -6.11817    0.08575  -71.35   <2e-16 ***
LBDSGLSI     0.69198    0.01378   50.20   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 14587  on 26191  degrees of freedom
AIC: 14591

Number of Fisher Scoring iterations: 5

#glimpse(Glucoseserum_model)

Interesting there was no * for this LBDSGSI in the first logistic regression were we compare all the features.
Serum glucose levels here shows it is correlated to having diabetes or not with 3***

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = LBDSCRSI)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

Creatinine_model <- glm(DIQ010 ~ LBDSCRSI, data = nhanes, family = binomial)
summary(Creatinine_model)


Call:
glm(formula = DIQ010 ~ LBDSCRSI, family = binomial, data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.6735  -0.5192  -0.4903  -0.4628   2.2402  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.6688515  0.0532148  -50.15   <2e-16 ***
LBDSCRSI     0.0086365  0.0006157   14.03   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 19102  on 26191  degrees of freedom
AIC: 19106

Number of Fisher Scoring iterations: 5

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = BPXDI1)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes  +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

Protein_model <- glm(DIQ010 ~ BPXDI1, data = nhanes, family = binomial)
summary(Protein_model)


Call:
glm(formula = DIQ010 ~ BPXDI1, family = binomial, data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.5246  -0.5106  -0.5087  -0.5063   2.0828  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.0476370  0.1045780 -19.580   <2e-16 ***
BPXDI1       0.0009994  0.0014769   0.677    0.499    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 19379  on 26191  degrees of freedom
AIC: 19383

Number of Fisher Scoring iterations: 4

# scatterplot with jitter
log_nhanes <- ggplot(data = nhanes, aes(y = DIQ010, x = LBDSCHSI)) + 
  geom_jitter(width = 0, height = 0.05, alpha = 0.5)

# add logistic curve
log_nhanes  +
  geom_smooth(method = "glm", se = FALSE, method.args = list(family = "binomial"))

Cholesterol_model <- glm(DIQ010 ~ LBDSCHSI, data = nhanes, family = binomial)
summary(Cholesterol_model)


Call:
glm(formula = DIQ010 ~ LBDSCHSI, family = binomial, data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.7568  -0.5347  -0.4998  -0.4574   2.5327  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.07522    0.08954  -12.01   <2e-16 ***
LBDSCHSI    -0.18586    0.01831  -10.15   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 19273  on 26191  degrees of freedom
AIC: 19277

Number of Fisher Scoring iterations: 4

library(broom)
# Use broom::augment to augment the model  
aug_nhanesmodel <- augment(nhanesmodel) 
glimpse(aug_nhanesmodel)

Observations: 26,193
Variables: 43
$ DIQ010     <dbl> 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,…
$ INDFMPIR   <dbl> 4.65, 5.00, 5.00, 5.00, 0.46, 1.06, 1.22, 3.03, 1.76,…
$ RIAGENDR   <chr> "Female", "Male", "Female", "Male", "Male", "Female",…
$ RIDAGEYR   <dbl> 44, 70, 16, 19, 21, 16, 79, 59, 27, 44, 62, 38, 43, 7…
$ RIDRETH1   <chr> "Non-Hispanic Black", "Non-Hispanic White", "Non-Hisp…
$ DR1_300    <chr> "Much less than usual", "Usual", "Much less than usua…
$ DR1_320Z   <dbl> 192.56, 829.50, 118.50, 1539.20, 2577.38, 0.00, 2281.…
$ DR1TALCO   <dbl> 0.0, 40.8, 0.0, 0.0, 36.3, 0.0, 54.3, 0.0, 0.0, 0.0, …
$ DR1TCAFF   <dbl> 13, 260, 71, 0, 10, 121, 95, 249, 39, 218, 203, 132, …
$ DR1TCARB   <dbl> 233.73, 269.93, 238.62, 243.56, 243.38, 275.62, 294.9…
$ DR1TCHOL   <dbl> 48, 138, 132, 359, 80, 189, 98, 79, 1103, 36, 139, 51…
$ DR1TFIBE   <dbl> 6.4, 20.3, 8.3, 14.3, 10.2, 9.7, 30.3, 8.7, 15.2, 66.…
$ DR1TKCAL   <dbl> 1458, 2168, 1688, 2232, 2083, 2322, 2134, 1722, 2223,…
$ DR1TPROT   <dbl> 27.43, 75.81, 45.92, 95.17, 51.05, 84.28, 73.87, 40.2…
$ DR1TSFAT   <dbl> 18.274, 17.608, 18.362, 47.397, 21.908, 38.860, 8.661…
$ DR1TSODI   <dbl> 1426, 3708, 1937, 3289, 2959, 3090, 2031, 2006, 4155,…
$ DR1TSUGR   <dbl> 146.01, 111.54, 136.71, 92.63, 77.70, 152.66, 133.37,…
$ DR1TTFAT   <dbl> 50.86, 60.16, 63.84, 100.19, 74.98, 101.08, 39.96, 51…
$ BMXBMI     <dbl> 30.90, 24.74, 16.79, 22.57, 25.03, 18.28, 28.93, 29.5…
$ BPXDI1     <dbl> 74, 60, 58, 62, 74, 42, 74, 76, 62, 82, 80, 62, 92, 7…
$ BPXPLS     <dbl> 58, 62, 88, 68, 54, 70, 66, 56, 78, 74, 62, 62, 80, 5…
$ BPXSY1     <dbl> 144, 138, 120, 108, 116, 106, 144, 136, 94, 120, 154,…
$ LBDSBUSI   <dbl> 2.14, 8.93, 2.50, 4.28, 3.21, 3.93, 3.57, 5.71, 2.14,…
$ LBDSCHSI   <dbl> 2.664, 3.931, 3.853, 4.241, 4.267, 3.258, 4.836, 5.27…
$ LBDSCRSI   <dbl> 70.72, 106.08, 79.56, 70.72, 61.88, 61.88, 79.56, 79.…
$ LBDSGLSI   <dbl> 4.83, 8.60, 4.39, 4.22, 4.50, 4.83, 5.22, 4.55, 4.00,…
$ LBDSTPSI   <dbl> 69, 72, 78, 72, 73, 72, 75, 69, 64, 68, 72, 72, 76, 6…
$ LBDSTRSI   <dbl> 0.881, 0.666, 0.553, 1.118, 0.294, 0.632, 0.508, 1.24…
$ LBDTCSI    <dbl> 2.72, 3.80, 3.80, 2.79, 5.35, 3.26, 4.68, 5.30, 6.28,…
$ LBXGH      <dbl> 6.0, 7.1, 4.7, 4.7, 4.8, 5.0, 5.0, 5.8, 4.3, 4.6, 6.1…
$ LBXSAPSI   <dbl> 74, 48, 41, 47, 183, 104, 67, 99, 72, 75, 153, 44, 84…
$ LBXSBU     <dbl> 6, 25, 7, 12, 9, 11, 10, 16, 6, 18, 13, 10, 13, 11, 1…
$ LBXSNASI   <dbl> 137, 140, 137, 143, 139, 139, 139, 140, 139, 138, 139…
$ LBXSOSSI   <dbl> 271, 287, 271, 283, 275, 276, 276, 280, 274, 277, 277…
$ SLQ050     <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No"…
$ WHQ030     <chr> "Overweight,", "Overweight,", "Underweight, or", "Abo…
$ .fitted    <dbl> -2.0740109, 0.4336325, -5.7762650, -5.4491232, -5.854…
$ .se.fit    <dbl> 0.1427966, 0.1303179, 0.2028511, 0.2515243, 0.2686952…
$ .resid     <dbl> -0.48659613, 0.99965363, -0.07868262, -0.09263751, -0…
$ .hat       <dbl> 2.022924e-03, 4.052159e-03, 1.269036e-04, 2.699478e-0…
$ .sigma     <dbl> 0.6361871, 0.6361640, 0.6361940, 0.6361939, 0.6361940…
$ .cooksd    <dbl> 6.226199e-06, 6.458106e-05, 9.598435e-09, 2.832738e-0…
$ .std.resid <dbl> -0.48708905, 1.00168519, -0.07868762, -0.09265002, -0…

# Load the dplyr package
library(dplyr)
# Convert the hflights data.frame into a hflights tbl
nhanes1 <- as_tibble(nhanes)
head(nhanes1)

# A tibble: 6 x 38
  INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
     <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
1     4.65 Female         44 Non-His… Much l…     193.      0         13
2     5    Male           70 Non-His… Usual       830.     40.8      260
3     5    Female         16 Non-His… Much l…     118.      0         71
4     5    Male           19 Non-His… Usual      1539.      0          0
5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
6     1.06 Female         16 Non-His… Usual         0       0        121
# … with 30 more variables: DR1TCARB <dbl>, DR1TCHOL <dbl>,
#   DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>, DR1TSFAT <dbl>,
#   DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>, BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>, LBDSBUSI <dbl>,
#   LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>, LBDSTPSI <dbl>,
#   LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>, LBXSAPSI <dbl>,
#   LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>, DIQ010 <dbl>,
#   SLQ050 <chr>, WHQ030 <chr>, odds <dbl>, log_odds <dbl>

glycohemoglobin % above 6.5 your prediabetic

ggplot(nhanes, aes(x= LBXGH )) + geom_histogram(bins=100,alpha=0.5,fill='blue')

#post people in nhanes have diabetes

#this is blood glucose level mmol/L 
ggplot(nhanes, aes(x= LBDSGLSI )) + geom_histogram(bins=100,alpha=0.5,fill='blue')

#post people in nhanes have normal to high glucose serum level. normal glucose serum level is at 5.6 mmol/L

#this is bodymass index level normal is 23-25
ggplot(nhanes, aes(x= BMXBMI   )) + geom_histogram(bins=50,alpha=0.5,fill='blue')

#post people in nhanes have normal to high glucose bodymass level.

pl <-ggplot(nhanes,aes(x=LBXGH , y=DIQ010))
pl2 <- pl+ geom_point(aes(color=DR1TSUGR),size=2)
pl3 <- pl2 + scale_color_gradient(low='blue',high='red')+ geom_jitter( alpha = 0.2)
print(pl3)

#library(ISLR)
nhanes <- read_csv('nhanes.csv')

Parsed with column specification:
cols(
  .default = col_double(),
  RIAGENDR = col_character(),
  RIDRETH1 = col_character(),
  DR1_300 = col_character(),
  DIQ010 = col_character(),
  SLQ050 = col_character(),
  WHQ030 = col_character()
)

See spec(...) for full column specifications.

nhanes$DIQ010 <- ifelse(nhanes$DIQ010=='Yes', 1,0)
nhanes

# A tibble: 26,193 x 36
   INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
      <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
 1     4.65 Female         44 Non-His… Much l…     193.      0         13
 2     5    Male           70 Non-His… Usual       830.     40.8      260
 3     5    Female         16 Non-His… Much l…     118.      0         71
 4     5    Male           19 Non-His… Usual      1539.      0          0
 5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
 6     1.06 Female         16 Non-His… Usual         0       0        121
 7     1.22 Male           79 Non-His… Usual      2281.     54.3       95
 8     3.03 Female         59 Non-His… Much l…     974       0        249
 9     1.76 Female         27 Mexican… Usual       622.      0         39
10     1.03 Female         44 Other R… Usual      1421.      0        218
# … with 26,183 more rows, and 28 more variables: DR1TCARB <dbl>,
#   DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>,
#   DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>,
#   BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>,
#   LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>,
#   LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>,
#   LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>,
#   DIQ010 <dbl>, SLQ050 <chr>, WHQ030 <chr>

nhanesshort <- select(nhanes, DIQ010,LBXGH, INDFMPIR,INDFMPIR,RIDAGEYR,DR1TCAFF,DR1TFIBE, 
DR1TSODI,DR1TSUGR,BMXBMI,BPXDI1,BPXPLS,LBDSCHSI,LBDSCRSI,LBDSTRSI,LBXGH,LBXSAPSI
)
nhanesshort

# A tibble: 26,193 x 15
   DIQ010 LBXGH INDFMPIR RIDAGEYR DR1TCAFF DR1TFIBE DR1TSODI DR1TSUGR
    <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1      0   6       4.65       44       13      6.4     1426    146. 
 2      1   7.1     5          70      260     20.3     3708    112. 
 3      0   4.7     5          16       71      8.3     1937    137. 
 4      0   4.7     5          19        0     14.3     3289     92.6
 5      0   4.8     0.46       21       10     10.2     2959     77.7
 6      0   5       1.06       16      121      9.7     3090    153. 
 7      0   5       1.22       79       95     30.3     2031    133. 
 8      1   5.8     3.03       59      249      8.7     2006    166. 
 9      0   4.3     1.76       27       39     15.2     4155     76.0
10      0   4.6     1.03       44      218     66       3135    242. 
# … with 26,183 more rows, and 7 more variables: BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSTRSI <dbl>, LBXSAPSI <dbl>

modelnhanes <- glm(DIQ010 ~ ., data=nhanesshort, family = binomial )

summary(modelnhanes)


Call:
glm(formula = DIQ010 ~ ., family = binomial, data = nhanesshort)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.1992  -0.3434  -0.2016  -0.1202   3.9778  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.214e+01  3.227e-01 -37.603  < 2e-16 ***
LBXGH        1.467e+00  3.365e-02  43.601  < 2e-16 ***
INDFMPIR    -5.354e-02  1.643e-02  -3.259  0.00112 ** 
RIDAGEYR     4.115e-02  1.777e-03  23.151  < 2e-16 ***
DR1TCAFF     2.877e-04  1.180e-04   2.437  0.01482 *  
DR1TFIBE     7.339e-03  2.870e-03   2.557  0.01056 *  
DR1TSODI     3.402e-05  1.744e-05   1.951  0.05110 .  
DR1TSUGR    -5.628e-03  4.568e-04 -12.319  < 2e-16 ***
BMXBMI       5.372e-02  3.510e-03  15.306  < 2e-16 ***
BPXDI1      -4.779e-03  1.944e-03  -2.459  0.01395 *  
BPXPLS       5.384e-03  2.186e-03   2.463  0.01378 *  
LBDSCHSI    -4.699e-01  2.694e-02 -17.443  < 2e-16 ***
LBDSCRSI     3.803e-03  5.802e-04   6.554 5.60e-11 ***
LBDSTRSI     1.009e-01  2.034e-02   4.960 7.06e-07 ***
LBXSAPSI    -2.806e-03  1.050e-03  -2.672  0.00753 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 10809  on 26178  degrees of freedom
AIC: 10839

Number of Fisher Scoring iterations: 6

coef(modelnhanes)

  (Intercept)         LBXGH      INDFMPIR      RIDAGEYR      DR1TCAFF 
-1.213627e+01  1.467247e+00 -5.353540e-02  4.114984e-02  2.876642e-04 
     DR1TFIBE      DR1TSODI      DR1TSUGR        BMXBMI        BPXDI1 
 7.338571e-03  3.402456e-05 -5.627560e-03  5.372284e-02 -4.779081e-03 
       BPXPLS      LBDSCHSI      LBDSCRSI      LBDSTRSI      LBXSAPSI 
 5.383626e-03 -4.699318e-01  3.802579e-03  1.008589e-01 -2.806218e-03

smp_size <- floor(0.75 * nrow(nhanes))

print(smp_size)

[1] 19644

set.seed(123)
train_ind <- sample(seq_len(nrow(nhanes)), size = smp_size)
train <- nhanes[train_ind, ]
test <- nhanes[-train_ind, ]

glimpse(nhanes)

Observations: 26,193
Variables: 36
$ INDFMPIR <dbl> 4.65, 5.00, 5.00, 5.00, 0.46, 1.06, 1.22, 3.03, 1.76, 1…
$ RIAGENDR <chr> "Female", "Male", "Female", "Male", "Male", "Female", "…
$ RIDAGEYR <dbl> 44, 70, 16, 19, 21, 16, 79, 59, 27, 44, 62, 38, 43, 71,…
$ RIDRETH1 <chr> "Non-Hispanic Black", "Non-Hispanic White", "Non-Hispan…
$ DR1_300  <chr> "Much less than usual", "Usual", "Much less than usual"…
$ DR1_320Z <dbl> 192.56, 829.50, 118.50, 1539.20, 2577.38, 0.00, 2281.13…
$ DR1TALCO <dbl> 0.0, 40.8, 0.0, 0.0, 36.3, 0.0, 54.3, 0.0, 0.0, 0.0, 30…
$ DR1TCAFF <dbl> 13, 260, 71, 0, 10, 121, 95, 249, 39, 218, 203, 132, 3,…
$ DR1TCARB <dbl> 233.73, 269.93, 238.62, 243.56, 243.38, 275.62, 294.99,…
$ DR1TCHOL <dbl> 48, 138, 132, 359, 80, 189, 98, 79, 1103, 36, 139, 517,…
$ DR1TFIBE <dbl> 6.4, 20.3, 8.3, 14.3, 10.2, 9.7, 30.3, 8.7, 15.2, 66.0,…
$ DR1TKCAL <dbl> 1458, 2168, 1688, 2232, 2083, 2322, 2134, 1722, 2223, 3…
$ DR1TPROT <dbl> 27.43, 75.81, 45.92, 95.17, 51.05, 84.28, 73.87, 40.29,…
$ DR1TSFAT <dbl> 18.274, 17.608, 18.362, 47.397, 21.908, 38.860, 8.661, …
$ DR1TSODI <dbl> 1426, 3708, 1937, 3289, 2959, 3090, 2031, 2006, 4155, 3…
$ DR1TSUGR <dbl> 146.01, 111.54, 136.71, 92.63, 77.70, 152.66, 133.37, 1…
$ DR1TTFAT <dbl> 50.86, 60.16, 63.84, 100.19, 74.98, 101.08, 39.96, 51.2…
$ BMXBMI   <dbl> 30.90, 24.74, 16.79, 22.57, 25.03, 18.28, 28.93, 29.51,…
$ BPXDI1   <dbl> 74, 60, 58, 62, 74, 42, 74, 76, 62, 82, 80, 62, 92, 74,…
$ BPXPLS   <dbl> 58, 62, 88, 68, 54, 70, 66, 56, 78, 74, 62, 62, 80, 54,…
$ BPXSY1   <dbl> 144, 138, 120, 108, 116, 106, 144, 136, 94, 120, 154, 1…
$ LBDSBUSI <dbl> 2.14, 8.93, 2.50, 4.28, 3.21, 3.93, 3.57, 5.71, 2.14, 6…
$ LBDSCHSI <dbl> 2.664, 3.931, 3.853, 4.241, 4.267, 3.258, 4.836, 5.275,…
$ LBDSCRSI <dbl> 70.72, 106.08, 79.56, 70.72, 61.88, 61.88, 79.56, 79.56…
$ LBDSGLSI <dbl> 4.83, 8.60, 4.39, 4.22, 4.50, 4.83, 5.22, 4.55, 4.00, 4…
$ LBDSTPSI <dbl> 69, 72, 78, 72, 73, 72, 75, 69, 64, 68, 72, 72, 76, 66,…
$ LBDSTRSI <dbl> 0.881, 0.666, 0.553, 1.118, 0.294, 0.632, 0.508, 1.242,…
$ LBDTCSI  <dbl> 2.72, 3.80, 3.80, 2.79, 5.35, 3.26, 4.68, 5.30, 6.28, 5…
$ LBXGH    <dbl> 6.0, 7.1, 4.7, 4.7, 4.8, 5.0, 5.0, 5.8, 4.3, 4.6, 6.1, …
$ LBXSAPSI <dbl> 74, 48, 41, 47, 183, 104, 67, 99, 72, 75, 153, 44, 84, …
$ LBXSBU   <dbl> 6, 25, 7, 12, 9, 11, 10, 16, 6, 18, 13, 10, 13, 11, 12,…
$ LBXSNASI <dbl> 137, 140, 137, 143, 139, 139, 139, 140, 139, 138, 139, …
$ LBXSOSSI <dbl> 271, 287, 271, 283, 275, 276, 276, 280, 274, 277, 277, …
$ DIQ010   <dbl> 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0…
$ SLQ050   <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No", …
$ WHQ030   <chr> "Overweight,", "Overweight,", "Underweight, or", "About…

diabetes <-table(nhanes$DIQ010)
diabetes


    0     1 
23010  3183

round(prop.table(table(nhanes$DIQ010)), 2)


   0    1 
0.88 0.12

head(nhanes)

# A tibble: 6 x 36
  INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
     <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
1     4.65 Female         44 Non-His… Much l…     193.      0         13
2     5    Male           70 Non-His… Usual       830.     40.8      260
3     5    Female         16 Non-His… Much l…     118.      0         71
4     5    Male           19 Non-His… Usual      1539.      0          0
5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
6     1.06 Female         16 Non-His… Usual         0       0        121
# … with 28 more variables: DR1TCARB <dbl>, DR1TCHOL <dbl>,
#   DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>, DR1TSFAT <dbl>,
#   DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>, BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>, LBDSBUSI <dbl>,
#   LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>, LBDSTPSI <dbl>,
#   LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>, LBXSAPSI <dbl>,
#   LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>, DIQ010 <dbl>,
#   SLQ050 <chr>, WHQ030 <chr>

Train Test split

n <- nrow(nhanes)
n

[1] 26193

#rows
nrow(nhanes)

[1] 26193

#calculate 80% of the rows
n_train <- round(0.80 * n)
n_train

[1] 20954

set.seed(123)
#create an index that is 80% of the data
train_ind <- sample(1:n, n_train)

#seperate the trian protion 
nhanes_train <- nhanes[train_ind,]

#see if it worked but counting 

#using the "-" sign seperate the test portion 
nhanes_test <-  nhanes[-train_ind,]

mdlnhanes <- glm(DIQ010~ ., data = nhanes, family = 'binomial')
summary(mdlnhanes)


Call:
glm(formula = DIQ010 ~ ., family = "binomial", data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.2233  -0.3367  -0.1947  -0.1136   4.0299  

Coefficients:
                                              Estimate Std. Error z value
(Intercept)                                 -1.603e+01  1.811e+00  -8.852
INDFMPIR                                    -5.140e-02  1.731e-02  -2.970
RIAGENDRMale                                 4.960e-03  6.023e-02   0.082
RIDAGEYR                                     3.652e-02  2.114e-03  17.277
RIDRETH1Non-Hispanic Black                   1.288e-01  8.961e-02   1.437
RIDRETH1Non-Hispanic White                  -2.463e-01  8.338e-02  -2.954
RIDRETH1Other Hispanic                       2.465e-02  1.059e-01   0.233
RIDRETH1Other Race - Including Multi-Racial -3.790e-02  1.143e-01  -0.332
DR1_300Much more than usual                  8.695e-02  1.074e-01   0.809
DR1_300Usual                                 3.260e-02  6.906e-02   0.472
DR1_320Z                                     1.024e-05  2.356e-05   0.435
DR1TALCO                                     1.266e-02  1.065e-02   1.188
DR1TCAFF                                     4.228e-04  1.225e-04   3.451
DR1TCARB                                     7.869e-03  6.367e-03   1.236
DR1TCHOL                                     1.678e-04  1.527e-04   1.099
DR1TFIBE                                     9.775e-03  4.853e-03   2.014
DR1TKCAL                                    -2.290e-03  1.536e-03  -1.490
DR1TPROT                                     5.844e-03  6.537e-03   0.894
DR1TSFAT                                    -9.169e-04  4.350e-03  -0.211
DR1TSODI                                     9.272e-05  2.848e-05   3.255
DR1TSUGR                                    -4.702e-03  9.907e-04  -4.746
DR1TTFAT                                     2.196e-02  1.338e-02   1.641
BMXBMI                                       4.021e-02  4.280e-03   9.394
BPXDI1                                      -5.066e-03  2.129e-03  -2.379
BPXPLS                                       4.583e-03  2.256e-03   2.031
BPXSY1                                       2.554e-03  1.576e-03   1.621
LBDSBUSI                                    -1.335e+01  9.003e+00  -1.483
LBDSCHSI                                    -3.444e-01  1.419e-01  -2.427
LBDSCRSI                                     2.345e-03  6.783e-04   3.457
LBDSGLSI                                     9.448e-02  5.519e-02   1.712
LBDSTPSI                                     2.476e-03  5.809e-03   0.426
LBDSTRSI                                     9.993e-02  2.196e-02   4.550
LBDTCSI                                     -1.270e-01  1.446e-01  -0.878
LBXGH                                        1.306e+00  4.252e-02  30.718
LBXSAPSI                                    -3.381e-03  1.109e-03  -3.049
LBXSBU                                       4.783e+00  3.214e+00   1.488
LBXSNASI                                     1.288e-02  9.791e-02   0.132
LBXSOSSI                                     8.642e-03  5.194e-02   0.166
SLQ050Yes                                    5.736e-01  5.550e-02  10.335
WHQ030Overweight,                            2.316e-01  6.783e-02   3.415
WHQ030Underweight, or                        1.147e-01  1.477e-01   0.777
                                            Pr(>|z|)    
(Intercept)                                  < 2e-16 ***
INDFMPIR                                    0.002976 ** 
RIAGENDRMale                                0.934366    
RIDAGEYR                                     < 2e-16 ***
RIDRETH1Non-Hispanic Black                  0.150709    
RIDRETH1Non-Hispanic White                  0.003132 ** 
RIDRETH1Other Hispanic                      0.815940    
RIDRETH1Other Race - Including Multi-Racial 0.740169    
DR1_300Much more than usual                 0.418287    
DR1_300Usual                                0.636910    
DR1_320Z                                    0.663761    
DR1TALCO                                    0.234663    
DR1TCAFF                                    0.000559 ***
DR1TCARB                                    0.216486    
DR1TCHOL                                    0.271842    
DR1TFIBE                                    0.043984 *  
DR1TKCAL                                    0.136155    
DR1TPROT                                    0.371330    
DR1TSFAT                                    0.833072    
DR1TSODI                                    0.001133 ** 
DR1TSUGR                                    2.07e-06 ***
DR1TTFAT                                    0.100868    
BMXBMI                                       < 2e-16 ***
BPXDI1                                      0.017339 *  
BPXPLS                                      0.042230 *  
BPXSY1                                      0.105036    
LBDSBUSI                                    0.138128    
LBDSCHSI                                    0.015232 *  
LBDSCRSI                                    0.000546 ***
LBDSGLSI                                    0.086907 .  
LBDSTPSI                                    0.669937    
LBDSTRSI                                    5.36e-06 ***
LBDTCSI                                     0.380017    
LBXGH                                        < 2e-16 ***
LBXSAPSI                                    0.002297 ** 
LBXSBU                                      0.136689    
LBXSNASI                                    0.895328    
LBXSOSSI                                    0.867862    
SLQ050Yes                                    < 2e-16 ***
WHQ030Overweight,                           0.000639 ***
WHQ030Underweight, or                       0.437320    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 10584  on 26152  degrees of freedom
AIC: 10666

Number of Fisher Scoring iterations: 6

library(tidyverse)
#nhanes_df <- read_csv('nhanes.csv') %>% 
 # mutate(odds = nhanes/(1 - nhanes),
  #      log_odds = log(odds)
   #   )
#glimpse(nhanes_df)

Random Forest

#  Do not change the code in this chunk!
nhanes <- read_csv('nhanes.csv')

Parsed with column specification:
cols(
  .default = col_double(),
  RIAGENDR = col_character(),
  RIDRETH1 = col_character(),
  DR1_300 = col_character(),
  DIQ010 = col_character(),
  SLQ050 = col_character(),
  WHQ030 = col_character()
)

See spec(...) for full column specifications.

nhanes$DIQ010 <- ifelse(nhanes$DIQ010=='Yes', 1,0)
nhanes

# A tibble: 26,193 x 36
   INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
      <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
 1     4.65 Female         44 Non-His… Much l…     193.      0         13
 2     5    Male           70 Non-His… Usual       830.     40.8      260
 3     5    Female         16 Non-His… Much l…     118.      0         71
 4     5    Male           19 Non-His… Usual      1539.      0          0
 5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
 6     1.06 Female         16 Non-His… Usual         0       0        121
 7     1.22 Male           79 Non-His… Usual      2281.     54.3       95
 8     3.03 Female         59 Non-His… Much l…     974       0        249
 9     1.76 Female         27 Mexican… Usual       622.      0         39
10     1.03 Female         44 Other R… Usual      1421.      0        218
# … with 26,183 more rows, and 28 more variables: DR1TCARB <dbl>,
#   DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>,
#   DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>,
#   BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>,
#   LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>,
#   LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>,
#   LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>,
#   DIQ010 <dbl>, SLQ050 <chr>, WHQ030 <chr>

nhanesshort <- select(nhanes, DIQ010,LBXGH, INDFMPIR,INDFMPIR,RIDAGEYR,DR1TCAFF,DR1TFIBE, 
DR1TSODI,DR1TSUGR,BMXBMI,BPXDI1,BPXPLS,LBDSCHSI,LBDSCRSI,LBDSTRSI,LBXGH,LBXSAPSI
)
nhanesshort

# A tibble: 26,193 x 15
   DIQ010 LBXGH INDFMPIR RIDAGEYR DR1TCAFF DR1TFIBE DR1TSODI DR1TSUGR
    <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1      0   6       4.65       44       13      6.4     1426    146. 
 2      1   7.1     5          70      260     20.3     3708    112. 
 3      0   4.7     5          16       71      8.3     1937    137. 
 4      0   4.7     5          19        0     14.3     3289     92.6
 5      0   4.8     0.46       21       10     10.2     2959     77.7
 6      0   5       1.06       16      121      9.7     3090    153. 
 7      0   5       1.22       79       95     30.3     2031    133. 
 8      1   5.8     3.03       59      249      8.7     2006    166. 
 9      0   4.3     1.76       27       39     15.2     4155     76.0
10      0   4.6     1.03       44      218     66       3135    242. 
# … with 26,183 more rows, and 7 more variables: BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSTRSI <dbl>, LBXSAPSI <dbl>

# Total number of rows in the credit data frame
n <- nrow(nhanesshort)

# Number of rows for the training set (80% of the dataset)
n_train <- round(0.8 * n) 

# Create a vector of indices which is an 80% random sample
set.seed(123)
train_nhanes <- sample(1:n, n_train)

# Subset the credit data frame to training indices only
nhanes_train <- nhanesshort[train_nhanes, ]  
  
# Exclude the training indices to create the test set
nhanes_test <- nhanesshort[-train_nhanes, ]

library(rpart)
library(rpart.plot)
tree<-rpart(DIQ010~., method="class",data=nhanes)
printcp(tree)


Classification tree:
rpart(formula = DIQ010 ~ ., data = nhanes, method = "class")

Variables actually used in tree construction:
[1] LBDTCSI LBXGH  

Root node error: 3183/26193 = 0.12152

n= 26193 

        CP nsplit rel error  xerror     xstd
1 0.380773      0   1.00000 1.00000 0.016613
2 0.028275      1   0.61923 0.61923 0.013413
3 0.010000      3   0.56268 0.56425 0.012850

plot(tree,uniform = T,main="nhanes Tree")
text(tree,use.n=T,all=T)

prp(tree)

tree<-rpart(DIQ010~., method="class",data=nhanes_train)
tree.preds<-predict(tree,nhanes_test)
head(tree.preds)

         0          1
1 0.953536 0.04646399
2 0.953536 0.04646399
3 0.953536 0.04646399
4 0.953536 0.04646399
5 0.953536 0.04646399
6 0.953536 0.04646399

#train model
tree<-rpart(DIQ010~., method="class",data=nhanes_train)
tree.preds<-predict(tree,nhanes_test)
tree.pred<-as.data.frame(tree.preds)
joiner<- function(x){
  if(x>=0.5){
    return('Yes')
  }else{
    return('No')
  }
}
tree.preds$DIQ010 <- sapply(tree.pred$Yes,joiner)

Warning in tree.preds$DIQ010 <- sapply(tree.pred$Yes, joiner): Coercing LHS
to a list

print(head(tree.preds))

[[1]]
[1] 0.953536

[[2]]
[1] 0.953536

[[3]]
[1] 0.953536

[[4]]
[1] 0.953536

[[5]]
[1] 0.953536

[[6]]
[1] 0.953536

table(tree.preds$DIQ010,tree.pred$DIQ010)

< table of extent 0 x 0 >

library(randomForest)

randomForest 4.6-14

Type rfNews() to see new features/changes/bug fixes.


Attaching package: 'randomForest'

The following object is masked from 'package:psych':

    outlier

The following object is masked from 'package:dplyr':

    combine

The following object is masked from 'package:ggplot2':

    margin

library(dplyr)
#nhanesshort$DIQ010 <- ifelse(nhanesshort$DIQ010=='Yes', 1,0)
nhanesshort

# A tibble: 26,193 x 15
   DIQ010 LBXGH INDFMPIR RIDAGEYR DR1TCAFF DR1TFIBE DR1TSODI DR1TSUGR
    <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1      0   6       4.65       44       13      6.4     1426    146. 
 2      1   7.1     5          70      260     20.3     3708    112. 
 3      0   4.7     5          16       71      8.3     1937    137. 
 4      0   4.7     5          19        0     14.3     3289     92.6
 5      0   4.8     0.46       21       10     10.2     2959     77.7
 6      0   5       1.06       16      121      9.7     3090    153. 
 7      0   5       1.22       79       95     30.3     2031    133. 
 8      1   5.8     3.03       59      249      8.7     2006    166. 
 9      0   4.3     1.76       27       39     15.2     4155     76.0
10      0   4.6     1.03       44      218     66       3135    242. 
# … with 26,183 more rows, and 7 more variables: BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSTRSI <dbl>, LBXSAPSI <dbl>

#data_fac=nhanesshort %>% mutate_if(is.character, as.factor)
#data_fac

rfn.model<-randomForest(DIQ010~., data=nhanesshort)

Warning in randomForest.default(m, y, ...): The response has five or fewer
unique values. Are you sure you want to do regression?

print(rfn.model)


Call:
 randomForest(formula = DIQ010 ~ ., data = nhanesshort) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 4

          Mean of squared residuals: 0.05378079
                    % Var explained: 49.62

rfn.model$confusion

NULL

rfn.model$importance

         IncNodePurity
LBXGH       1146.71523
INDFMPIR      85.85677
RIDAGEYR     199.99036
DR1TCAFF      89.54424
DR1TFIBE      97.29164
DR1TSODI     102.08023
DR1TSUGR     137.18158
BMXBMI       150.21798
BPXDI1        82.16728
BPXPLS        75.28521
LBDSCHSI     158.98412
LBDSCRSI     118.87952
LBDSTRSI     105.85056
LBXSAPSI      89.56121

#rfn.preds<-predict(rfn.model,nhanes_test)
#table(rfn.preds,nhanes_test$DIQ010)

library(ranger)


Attaching package: 'ranger'

The following object is masked from 'package:randomForest':

    importance

library(caret)
library(mlbench)

f_model <- train(
  DIQ010 ~ .,
  tuneLength = 3,
  data = nhanes_train, method = "ranger",
  trControl = trainControl(method = "cv", number = 10, verboseIter = TRUE)
)

Warning in train.default(x, y, weights = w, ...): You are trying to do
regression and your outcome only has two possible values Are you trying to
do classification? If so, use a 2 level factor as your outcome column.

+ Fold01: mtry= 2, min.node.size=5, splitrule=variance 
- Fold01: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold01: mtry= 8, min.node.size=5, splitrule=variance 
- Fold01: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold01: mtry=14, min.node.size=5, splitrule=variance 
- Fold01: mtry=14, min.node.size=5, splitrule=variance 
+ Fold01: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold01: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold01: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold01: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold01: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold01: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold02: mtry= 2, min.node.size=5, splitrule=variance 
- Fold02: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold02: mtry= 8, min.node.size=5, splitrule=variance 
- Fold02: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold02: mtry=14, min.node.size=5, splitrule=variance 
- Fold02: mtry=14, min.node.size=5, splitrule=variance 
+ Fold02: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold02: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold02: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold02: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold02: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold02: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold03: mtry= 2, min.node.size=5, splitrule=variance 
- Fold03: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold03: mtry= 8, min.node.size=5, splitrule=variance 
- Fold03: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold03: mtry=14, min.node.size=5, splitrule=variance 
- Fold03: mtry=14, min.node.size=5, splitrule=variance 
+ Fold03: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold03: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold03: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold03: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold03: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold03: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold04: mtry= 2, min.node.size=5, splitrule=variance 
- Fold04: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold04: mtry= 8, min.node.size=5, splitrule=variance 
- Fold04: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold04: mtry=14, min.node.size=5, splitrule=variance 
- Fold04: mtry=14, min.node.size=5, splitrule=variance 
+ Fold04: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold04: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold04: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold04: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold04: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold04: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold05: mtry= 2, min.node.size=5, splitrule=variance 
- Fold05: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold05: mtry= 8, min.node.size=5, splitrule=variance 
- Fold05: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold05: mtry=14, min.node.size=5, splitrule=variance 
- Fold05: mtry=14, min.node.size=5, splitrule=variance 
+ Fold05: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold05: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold05: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold05: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold05: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold05: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold06: mtry= 2, min.node.size=5, splitrule=variance 
- Fold06: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold06: mtry= 8, min.node.size=5, splitrule=variance 
- Fold06: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold06: mtry=14, min.node.size=5, splitrule=variance 
- Fold06: mtry=14, min.node.size=5, splitrule=variance 
+ Fold06: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold06: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold06: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold06: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold06: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold06: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold07: mtry= 2, min.node.size=5, splitrule=variance 
- Fold07: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold07: mtry= 8, min.node.size=5, splitrule=variance 
- Fold07: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold07: mtry=14, min.node.size=5, splitrule=variance 
- Fold07: mtry=14, min.node.size=5, splitrule=variance 
+ Fold07: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold07: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold07: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold07: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold07: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold07: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold08: mtry= 2, min.node.size=5, splitrule=variance 
- Fold08: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold08: mtry= 8, min.node.size=5, splitrule=variance 
- Fold08: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold08: mtry=14, min.node.size=5, splitrule=variance 
- Fold08: mtry=14, min.node.size=5, splitrule=variance 
+ Fold08: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold08: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold08: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold08: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold08: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold08: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold09: mtry= 2, min.node.size=5, splitrule=variance 
- Fold09: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold09: mtry= 8, min.node.size=5, splitrule=variance 
- Fold09: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold09: mtry=14, min.node.size=5, splitrule=variance 
- Fold09: mtry=14, min.node.size=5, splitrule=variance 
+ Fold09: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold09: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold09: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold09: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold09: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold09: mtry=14, min.node.size=5, splitrule=extratrees 
+ Fold10: mtry= 2, min.node.size=5, splitrule=variance 
- Fold10: mtry= 2, min.node.size=5, splitrule=variance 
+ Fold10: mtry= 8, min.node.size=5, splitrule=variance 
- Fold10: mtry= 8, min.node.size=5, splitrule=variance 
+ Fold10: mtry=14, min.node.size=5, splitrule=variance 
- Fold10: mtry=14, min.node.size=5, splitrule=variance 
+ Fold10: mtry= 2, min.node.size=5, splitrule=extratrees 
- Fold10: mtry= 2, min.node.size=5, splitrule=extratrees 
+ Fold10: mtry= 8, min.node.size=5, splitrule=extratrees 
- Fold10: mtry= 8, min.node.size=5, splitrule=extratrees 
+ Fold10: mtry=14, min.node.size=5, splitrule=extratrees 
- Fold10: mtry=14, min.node.size=5, splitrule=extratrees 
Aggregating results
Selecting tuning parameters
Fitting mtry = 8, splitrule = extratrees, min.node.size = 5 on full training set

Train Test split

library(tidyverse)
glimpse(nhanes)

Observations: 26,193
Variables: 36
$ INDFMPIR <dbl> 4.65, 5.00, 5.00, 5.00, 0.46, 1.06, 1.22, 3.03, 1.76, 1…
$ RIAGENDR <chr> "Female", "Male", "Female", "Male", "Male", "Female", "…
$ RIDAGEYR <dbl> 44, 70, 16, 19, 21, 16, 79, 59, 27, 44, 62, 38, 43, 71,…
$ RIDRETH1 <chr> "Non-Hispanic Black", "Non-Hispanic White", "Non-Hispan…
$ DR1_300  <chr> "Much less than usual", "Usual", "Much less than usual"…
$ DR1_320Z <dbl> 192.56, 829.50, 118.50, 1539.20, 2577.38, 0.00, 2281.13…
$ DR1TALCO <dbl> 0.0, 40.8, 0.0, 0.0, 36.3, 0.0, 54.3, 0.0, 0.0, 0.0, 30…
$ DR1TCAFF <dbl> 13, 260, 71, 0, 10, 121, 95, 249, 39, 218, 203, 132, 3,…
$ DR1TCARB <dbl> 233.73, 269.93, 238.62, 243.56, 243.38, 275.62, 294.99,…
$ DR1TCHOL <dbl> 48, 138, 132, 359, 80, 189, 98, 79, 1103, 36, 139, 517,…
$ DR1TFIBE <dbl> 6.4, 20.3, 8.3, 14.3, 10.2, 9.7, 30.3, 8.7, 15.2, 66.0,…
$ DR1TKCAL <dbl> 1458, 2168, 1688, 2232, 2083, 2322, 2134, 1722, 2223, 3…
$ DR1TPROT <dbl> 27.43, 75.81, 45.92, 95.17, 51.05, 84.28, 73.87, 40.29,…
$ DR1TSFAT <dbl> 18.274, 17.608, 18.362, 47.397, 21.908, 38.860, 8.661, …
$ DR1TSODI <dbl> 1426, 3708, 1937, 3289, 2959, 3090, 2031, 2006, 4155, 3…
$ DR1TSUGR <dbl> 146.01, 111.54, 136.71, 92.63, 77.70, 152.66, 133.37, 1…
$ DR1TTFAT <dbl> 50.86, 60.16, 63.84, 100.19, 74.98, 101.08, 39.96, 51.2…
$ BMXBMI   <dbl> 30.90, 24.74, 16.79, 22.57, 25.03, 18.28, 28.93, 29.51,…
$ BPXDI1   <dbl> 74, 60, 58, 62, 74, 42, 74, 76, 62, 82, 80, 62, 92, 74,…
$ BPXPLS   <dbl> 58, 62, 88, 68, 54, 70, 66, 56, 78, 74, 62, 62, 80, 54,…
$ BPXSY1   <dbl> 144, 138, 120, 108, 116, 106, 144, 136, 94, 120, 154, 1…
$ LBDSBUSI <dbl> 2.14, 8.93, 2.50, 4.28, 3.21, 3.93, 3.57, 5.71, 2.14, 6…
$ LBDSCHSI <dbl> 2.664, 3.931, 3.853, 4.241, 4.267, 3.258, 4.836, 5.275,…
$ LBDSCRSI <dbl> 70.72, 106.08, 79.56, 70.72, 61.88, 61.88, 79.56, 79.56…
$ LBDSGLSI <dbl> 4.83, 8.60, 4.39, 4.22, 4.50, 4.83, 5.22, 4.55, 4.00, 4…
$ LBDSTPSI <dbl> 69, 72, 78, 72, 73, 72, 75, 69, 64, 68, 72, 72, 76, 66,…
$ LBDSTRSI <dbl> 0.881, 0.666, 0.553, 1.118, 0.294, 0.632, 0.508, 1.242,…
$ LBDTCSI  <dbl> 2.72, 3.80, 3.80, 2.79, 5.35, 3.26, 4.68, 5.30, 6.28, 5…
$ LBXGH    <dbl> 6.0, 7.1, 4.7, 4.7, 4.8, 5.0, 5.0, 5.8, 4.3, 4.6, 6.1, …
$ LBXSAPSI <dbl> 74, 48, 41, 47, 183, 104, 67, 99, 72, 75, 153, 44, 84, …
$ LBXSBU   <dbl> 6, 25, 7, 12, 9, 11, 10, 16, 6, 18, 13, 10, 13, 11, 12,…
$ LBXSNASI <dbl> 137, 140, 137, 143, 139, 139, 139, 140, 139, 138, 139, …
$ LBXSOSSI <dbl> 271, 287, 271, 283, 275, 276, 276, 280, 274, 277, 277, …
$ DIQ010   <dbl> 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0…
$ SLQ050   <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No", …
$ WHQ030   <chr> "Overweight,", "Overweight,", "Underweight, or", "About…

n <- nrow(nhanesshort)
n

[1] 26193

#rows
nrow(nhanesshort)

[1] 26193

#calculate 80% of the rows
n_train <- round(0.80 * n)
n_train

[1] 20954

set.seed(123)
#create an index that is 80% of the data
train_ind <- sample(1:n, n_train)

#seperate the trian protion 
nhanes_train <- nhanesshort[train_ind,]

#see if it worked but counting 

#using the "-" sign seperate the test portion 
nhanes_test <-  nhanesshort[-train_ind,]

mdlnhanes <- glm(DIQ010~ ., data = nhanes, family = 'binomial')
summary(mdlnhanes)


Call:
glm(formula = DIQ010 ~ ., family = "binomial", data = nhanes)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.2233  -0.3367  -0.1947  -0.1136   4.0299  

Coefficients:
                                              Estimate Std. Error z value
(Intercept)                                 -1.603e+01  1.811e+00  -8.852
INDFMPIR                                    -5.140e-02  1.731e-02  -2.970
RIAGENDRMale                                 4.960e-03  6.023e-02   0.082
RIDAGEYR                                     3.652e-02  2.114e-03  17.277
RIDRETH1Non-Hispanic Black                   1.288e-01  8.961e-02   1.437
RIDRETH1Non-Hispanic White                  -2.463e-01  8.338e-02  -2.954
RIDRETH1Other Hispanic                       2.465e-02  1.059e-01   0.233
RIDRETH1Other Race - Including Multi-Racial -3.790e-02  1.143e-01  -0.332
DR1_300Much more than usual                  8.695e-02  1.074e-01   0.809
DR1_300Usual                                 3.260e-02  6.906e-02   0.472
DR1_320Z                                     1.024e-05  2.356e-05   0.435
DR1TALCO                                     1.266e-02  1.065e-02   1.188
DR1TCAFF                                     4.228e-04  1.225e-04   3.451
DR1TCARB                                     7.869e-03  6.367e-03   1.236
DR1TCHOL                                     1.678e-04  1.527e-04   1.099
DR1TFIBE                                     9.775e-03  4.853e-03   2.014
DR1TKCAL                                    -2.290e-03  1.536e-03  -1.490
DR1TPROT                                     5.844e-03  6.537e-03   0.894
DR1TSFAT                                    -9.169e-04  4.350e-03  -0.211
DR1TSODI                                     9.272e-05  2.848e-05   3.255
DR1TSUGR                                    -4.702e-03  9.907e-04  -4.746
DR1TTFAT                                     2.196e-02  1.338e-02   1.641
BMXBMI                                       4.021e-02  4.280e-03   9.394
BPXDI1                                      -5.066e-03  2.129e-03  -2.379
BPXPLS                                       4.583e-03  2.256e-03   2.031
BPXSY1                                       2.554e-03  1.576e-03   1.621
LBDSBUSI                                    -1.335e+01  9.003e+00  -1.483
LBDSCHSI                                    -3.444e-01  1.419e-01  -2.427
LBDSCRSI                                     2.345e-03  6.783e-04   3.457
LBDSGLSI                                     9.448e-02  5.519e-02   1.712
LBDSTPSI                                     2.476e-03  5.809e-03   0.426
LBDSTRSI                                     9.993e-02  2.196e-02   4.550
LBDTCSI                                     -1.270e-01  1.446e-01  -0.878
LBXGH                                        1.306e+00  4.252e-02  30.718
LBXSAPSI                                    -3.381e-03  1.109e-03  -3.049
LBXSBU                                       4.783e+00  3.214e+00   1.488
LBXSNASI                                     1.288e-02  9.791e-02   0.132
LBXSOSSI                                     8.642e-03  5.194e-02   0.166
SLQ050Yes                                    5.736e-01  5.550e-02  10.335
WHQ030Overweight,                            2.316e-01  6.783e-02   3.415
WHQ030Underweight, or                        1.147e-01  1.477e-01   0.777
                                            Pr(>|z|)    
(Intercept)                                  < 2e-16 ***
INDFMPIR                                    0.002976 ** 
RIAGENDRMale                                0.934366    
RIDAGEYR                                     < 2e-16 ***
RIDRETH1Non-Hispanic Black                  0.150709    
RIDRETH1Non-Hispanic White                  0.003132 ** 
RIDRETH1Other Hispanic                      0.815940    
RIDRETH1Other Race - Including Multi-Racial 0.740169    
DR1_300Much more than usual                 0.418287    
DR1_300Usual                                0.636910    
DR1_320Z                                    0.663761    
DR1TALCO                                    0.234663    
DR1TCAFF                                    0.000559 ***
DR1TCARB                                    0.216486    
DR1TCHOL                                    0.271842    
DR1TFIBE                                    0.043984 *  
DR1TKCAL                                    0.136155    
DR1TPROT                                    0.371330    
DR1TSFAT                                    0.833072    
DR1TSODI                                    0.001133 ** 
DR1TSUGR                                    2.07e-06 ***
DR1TTFAT                                    0.100868    
BMXBMI                                       < 2e-16 ***
BPXDI1                                      0.017339 *  
BPXPLS                                      0.042230 *  
BPXSY1                                      0.105036    
LBDSBUSI                                    0.138128    
LBDSCHSI                                    0.015232 *  
LBDSCRSI                                    0.000546 ***
LBDSGLSI                                    0.086907 .  
LBDSTPSI                                    0.669937    
LBDSTRSI                                    5.36e-06 ***
LBDTCSI                                     0.380017    
LBXGH                                        < 2e-16 ***
LBXSAPSI                                    0.002297 ** 
LBXSBU                                      0.136689    
LBXSNASI                                    0.895328    
LBXSOSSI                                    0.867862    
SLQ050Yes                                    < 2e-16 ***
WHQ030Overweight,                           0.000639 ***
WHQ030Underweight, or                       0.437320    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 19380  on 26192  degrees of freedom
Residual deviance: 10584  on 26152  degrees of freedom
AIC: 10666

Number of Fisher Scoring iterations: 6

Random Forest model

The idea in random forests is to improve the variance reduction of bagging by reducing the correlation between the trees, without increasing the variance too much. This is achieved in the tree-growing process through random selection of the input variables.This method will have no incremental increase in bias due to this model.

library(randomForest)
library(caTools)
library(rpart)
#library(caret)
#library(CART)
#train a default RF model (500 trees)
#modelsRF <- randomForest(formula=DIQ010~., data = nhanes)
modelsRF<-randomForest(LBXGH~.,
        data=nhanes_train,
        importance=TRUE,
        prOximity=TRUE)
# Train a Random Forest
#set.seed(1)  # for reproducibility
#modelsRF <- randomForest(formula =LBXGH ~ ., data = nhanes_train)
                             
# Print the model output                             
print(modelsRF)


Call:
 randomForest(formula = LBXGH ~ ., data = nhanes_train, importance = TRUE,      prOximity = TRUE) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 4

          Mean of squared residuals: 0.6006228
                    % Var explained: 43.04

str(nhanes)

Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame':    26193 obs. of  36 variables:
 $ INDFMPIR: num  4.65 5 5 5 0.46 1.06 1.22 3.03 1.76 1.03 ...
 $ RIAGENDR: chr  "Female" "Male" "Female" "Male" ...
 $ RIDAGEYR: num  44 70 16 19 21 16 79 59 27 44 ...
 $ RIDRETH1: chr  "Non-Hispanic Black" "Non-Hispanic White" "Non-Hispanic Black" "Non-Hispanic White" ...
 $ DR1_300 : chr  "Much less than usual" "Usual" "Much less than usual" "Usual" ...
 $ DR1_320Z: num  193 830 118 1539 2577 ...
 $ DR1TALCO: num  0 40.8 0 0 36.3 0 54.3 0 0 0 ...
 $ DR1TCAFF: num  13 260 71 0 10 121 95 249 39 218 ...
 $ DR1TCARB: num  234 270 239 244 243 ...
 $ DR1TCHOL: num  48 138 132 359 80 ...
 $ DR1TFIBE: num  6.4 20.3 8.3 14.3 10.2 9.7 30.3 8.7 15.2 66 ...
 $ DR1TKCAL: num  1458 2168 1688 2232 2083 ...
 $ DR1TPROT: num  27.4 75.8 45.9 95.2 51 ...
 $ DR1TSFAT: num  18.3 17.6 18.4 47.4 21.9 ...
 $ DR1TSODI: num  1426 3708 1937 3289 2959 ...
 $ DR1TSUGR: num  146 111.5 136.7 92.6 77.7 ...
 $ DR1TTFAT: num  50.9 60.2 63.8 100.2 75 ...
 $ BMXBMI  : num  30.9 24.7 16.8 22.6 25 ...
 $ BPXDI1  : num  74 60 58 62 74 42 74 76 62 82 ...
 $ BPXPLS  : num  58 62 88 68 54 70 66 56 78 74 ...
 $ BPXSY1  : num  144 138 120 108 116 106 144 136 94 120 ...
 $ LBDSBUSI: num  2.14 8.93 2.5 4.28 3.21 3.93 3.57 5.71 2.14 6.43 ...
 $ LBDSCHSI: num  2.66 3.93 3.85 4.24 4.27 ...
 $ LBDSCRSI: num  70.7 106.1 79.6 70.7 61.9 ...
 $ LBDSGLSI: num  4.83 8.6 4.39 4.22 4.5 4.83 5.22 4.55 4 4.88 ...
 $ LBDSTPSI: num  69 72 78 72 73 72 75 69 64 68 ...
 $ LBDSTRSI: num  0.881 0.666 0.553 1.118 0.294 ...
 $ LBDTCSI : num  2.72 3.8 3.8 2.79 5.35 3.26 4.68 5.3 6.28 5.12 ...
 $ LBXGH   : num  6 7.1 4.7 4.7 4.8 5 5 5.8 4.3 4.6 ...
 $ LBXSAPSI: num  74 48 41 47 183 104 67 99 72 75 ...
 $ LBXSBU  : num  6 25 7 12 9 11 10 16 6 18 ...
 $ LBXSNASI: num  137 140 137 143 139 139 139 140 139 138 ...
 $ LBXSOSSI: num  271 287 271 283 275 276 276 280 274 277 ...
 $ DIQ010  : num  0 1 0 0 0 0 0 1 0 0 ...
 $ SLQ050  : chr  "No" "No" "No" "No" ...
 $ WHQ030  : chr  "Overweight," "Overweight," "Underweight, or" "About the right weight?" ...
 - attr(*, "spec")=
  .. cols(
  ..   INDFMPIR = col_double(),
  ..   RIAGENDR = col_character(),
  ..   RIDAGEYR = col_double(),
  ..   RIDRETH1 = col_character(),
  ..   DR1_300 = col_character(),
  ..   DR1_320Z = col_double(),
  ..   DR1TALCO = col_double(),
  ..   DR1TCAFF = col_double(),
  ..   DR1TCARB = col_double(),
  ..   DR1TCHOL = col_double(),
  ..   DR1TFIBE = col_double(),
  ..   DR1TKCAL = col_double(),
  ..   DR1TPROT = col_double(),
  ..   DR1TSFAT = col_double(),
  ..   DR1TSODI = col_double(),
  ..   DR1TSUGR = col_double(),
  ..   DR1TTFAT = col_double(),
  ..   BMXBMI = col_double(),
  ..   BPXDI1 = col_double(),
  ..   BPXPLS = col_double(),
  ..   BPXSY1 = col_double(),
  ..   LBDSBUSI = col_double(),
  ..   LBDSCHSI = col_double(),
  ..   LBDSCRSI = col_double(),
  ..   LBDSGLSI = col_double(),
  ..   LBDSTPSI = col_double(),
  ..   LBDSTRSI = col_double(),
  ..   LBDTCSI = col_double(),
  ..   LBXGH = col_double(),
  ..   LBXSAPSI = col_double(),
  ..   LBXSBU = col_double(),
  ..   LBXSNASI = col_double(),
  ..   LBXSOSSI = col_double(),
  ..   DIQ010 = col_character(),
  ..   SLQ050 = col_character(),
  ..   WHQ030 = col_character()
  .. )

#nhanesDIQ010<- ifelse(nhanes$DIQ010=="yes",1,0)
#nhanes

# Train a Random Forest
#set.seed(1)  # for reproducibility
#credit_model <- randomForest(formula = DIQ010 ~ ., 
#                             data = nhanes_train)
library(ranger)
rf <- ranger(LBXGH ~ ., data = nhanes_train, num.trees = 50, write.forest = TRUE)
getTerminalNodeIDs(rf, nhanes_train)

Warning in getTerminalNodeIDs(rf, nhanes_train): Function
getTerminalNodeIDs() deprecated, calling predict().

          [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11]
    [1,]  8424  4211 10728  6361  4723  7370  1882  2401  8625   476 10884
    [2,] 13153  9873  9511  6990 11678  9819  7139  4382  5950 11442  8784
    [3,]  4747 11632 10646  6019  7705  1205  2243  7019  7847  5203 11612
    [4,]  2787  2390  3975  8059   985  5485  5888  6679  5703  4091  7689
    [5,]  4013  2182  9849 11470  1517  6439 10894  3607 12657 13141 12940
    [6,]  4254 11529  6649 12054  4016  8579  4500 12633  9589 10980   559
    [7,]  2340 10657  7205  5290  9466  3952  4572  8616 11762  9185 13567
    [8,] 10235  8083  5018 12229  8901  4424  6976 12012 12042  4192  7867
    [9,] 11010  4486 13022  9958 13304 12717 12989 12477  2271  3342  9877
   [10,]  7083  5150  8531  4507  3824  1784  7910  7870  3834  4067 12546
   [11,]  1911  1968  4790  3736   829  2572  3027  1176  5319  5539  2661
   [12,]  2073  6972  4667  7025  5570 11918  2292  3873  8879 12964  9108
   [13,]  9045 12607 11456 11047 12044  9583  4556 13049  9654   198 10907
   [14,]  8229   830  1535  4806   132  1288  1086  2511  6630   792  1778
   [15,]  4538 12566  5222  8666  7638 11176  9680 12944 11055  9578  9771
   [16,]  6458 10358 13050 13319  7141 10239 11485 11022 12170  6067 13074
   [17,]  2931   146   320   101  2426   346   622  4267  1283  4149   230
   [18,]  6011  8204  1551  5996  7739  1307  4150  6856  4290  2046  3809
   [19,]  2520  3904  9854 11544 11361  3127  3240 10050 12933  8179  2853
   [20,] 13110  9986 12850  5505  2463  4143 13721 12796 13138  2591  5887
   [21,]  4819  1000  6936 10759  3360 11305   752  4557  1472 10413  3382
   [22,]  7603  4162 10585 13531  9168  8348  3528 11633 11841 10746  6636
   [23,]  9989 12123 10669 11159  9393  1015 12593 11276 10537 10357 12659
   [24,]  4407 10662  2390  6895  3029  3178 10978  7066 10232  6487  9683
   [25,]  4519 12083  9163  5704  9640  9646 11273 12289  3544  9254 11404
   [26,] 10238  2837  1724  9149   832  3421  7067  2565  2668   435  2706
   [27,] 11176 12789  9875 13506  7126 11006  5488  4202 10464  1625  4635
   [28,]  7575 11384 10949  3353  9525  4003 11136  8712  9990  4337  5222
   [29,]  9653 12409 10922 10832  8969 11955 13553 10019 12022  4760 12301
   [30,]  6198 10342  9271  9182 11274  8105  4256  6942 13369  2961 10311
   [31,] 10108  9102  2883  1009  8890  3612 11408  8897  4138  7582  4747
   [32,]  8267 13585  9774  4852 12168  9893  9978 10204  6170  7569  6545
   [33,] 11149  9925 10185  8555  7418  2835  3693 10185  9972  2557  1583
   [34,] 11532 10585 13285 13528  2747  5162 10851 12678 12682  9927 12677
   [35,]  8083 10097  8844  8886 10476 11857  8790 12220 12272 10363  4187
   [36,]   390 10839 10761  1647  8599  9618  8636 12348   317  6627 10038
   [37,]  4894  1819  3961  6389  5167  8204  4676 11224  3443  5260  1575
   [38,] 11626 12489  7119 13474  6054  1569 12810  8604  6733  2320 13386
   [39,]  9067  7993  6895  7890  4494  5452 10562  8498  6444   840 13544
   [40,]  8834 12614  3685  7743 11642 12977 13160 11922  5168 13038  9073
   [41,]  5642  9049  2695  6755  8687  7871  7133  8409 11245 11930  6935
   [42,]  3466  4305  1794  4290  6331  6150  9642  1727  9456  5339  5187
   [43,] 11907  9804 11640  2562  7409  7118 12179  3847  4769  7262 12455
   [44,] 10966 10078 12065  5669  5598  9828 13521  8478 13643 12784 11011
   [45,]  1129  6536  4883  8529 11541 10143  2781  1717  1349   133  3165
   [46,]   483 12593 11414  6007  3179  3083   622  9543  1827  8394  3120
   [47,] 12196  8022 10699  9804  4148 12900 10470  8415  6372 10854 13540
   [48,]  5834 10182  1870  1615  6776  6892  9016  9885  1148  2760  7742
   [49,]  9154  9860  3462 10646  7819 11908 10692  8843  4793  9578  8772
   [50,]  2815  4784  3134 10773  3528  4446  5953 12054   594 12156  3489
   [51,]  9885 12838 12453 12722  7193 12112  8347  1678  9784  8215  8968
   [52,] 12636  9075  6671  9871  6213 10422  5427  8622  5295 12742  9220
   [53,] 11610  8700 10821  5606 10833  6766  8221  8884  8789  3986 11698
   [54,] 12012 12798  8424  3119  9831 12905 10165 13169  5732  7916 11758
   [55,]  9198  7046  2545  7897   272  2399   658 10691  6172  1442  7583
   [56,]  8886  6200  2021 12145  1477  3681  9033  7329 12172 13349  5349
   [57,] 11201 13422 11611  4162  8370  6107  7509 12300  3449  3259 13352
   [58,] 13308  9179  5712  3840 11692 13082 10707  8117 13303 12699  9221
   [59,]  9535  2483 11717  7403  1565 11447  3397 11100  7006  9212  8362
   [60,] 10543  2545  2626  1136   689  9206  4478  1328  1275  3235   650
   [61,] 12667  1436   750  3484  5273  5385  1049  8930  7730  2100  3826
   [62,]  5576 11933 11380 10559  6073 12293  7923 11330  7284  3124 12546
   [63,] 11694 11026  4960  3643  1206  5443  3924  1891   654  6661  8881
   [64,]   351 11025  1875  3308  3166  1659  2857  5685  3012  2030   424
   [65,] 12605 12636 11474  9653 11061  6342 13750  8421 13643 10212 13271
   [66,]  4259 11206  8563 13363  8027 12958 12500 11002 12812 12904  7207
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 [1191,]  7457 12328 13157 13199 11274  5868 12764 11021 13057 12584  2160
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 [1193,] 12839  8417 10210 10510 13552 13432 13177 13540 13540 10559 12507
 [1194,] 12628  5794 10830  7849  4382  8919 13017 10251  9678  3304 13036
 [1195,]  1947 11616  6070  7971 12232  7763  8018  9828  2025  7692  7991
 [1196,] 13048 10558 10608 11046  6068 10976  8380 12682  7258  9151  9503
 [1197,] 13176  7194 13223 13400  5794 13574 13381  9183 10064  8862 11822
 [1198,]  8595 11511  7813 11133  7444  5093 11744  2006  5145 10842  5566
 [1199,]  8749 11537  9820  4918  4254 10956 13780  6587  1839  7378  1353
 [1200,]  8360  5172 10965  7347 12597  5834 13026  8227 10989 11191 12787
 [1201,] 10828  8712  3883  9421  5039  5033  1368 10874  3487  3250 12875
 [1202,]  6983  2814 12581  9665  5375  5380  2892  8993  6584 10428  7934
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 [1204,] 10788  8685 10032  6650  3004  4714  9763 10618  9672  1732 11586
 [1205,]   680  7537  9474  3747 11477  4408 11803 12452  7018  4051  6480
 [1206,]  5576  4465  7443  6897  7743  5813  4976 11385  8189 11570  9864
 [1207,] 10837  8041  6735 13278  3433  2777  1222 11210  9707  6610  3732
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 [1209,]  2581  3268  6870  2133  3945  9920  1565  6295  5319  9087  8989
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 [1211,]  1483  5894   767  2231  8852  9735  9017  2558  5638   255  9919
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 [1213,]  4567  4492 12741  2275  1273  4455 10606  4108   523 10916  4365
 [1214,]  3624  1311 10446  8078  5472  3602  8978   213  8467  7407 12110
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 [1216,]  4753  9212  2306 10775  6663  3423  8061  6879   941 12505  1296
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 [1221,]  5541  2709  4556  2596  5332  8620  8782 10533  7152  7650  8709
 [1222,] 10990  5932  5327  2772  4458  7675  5917  8960  7181    24  7742
 [1223,]  4569 12198  3587 10653  7901 11250 11855  6729  7533  8380  2575
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 [1228,]  9254 12436 11986 12747 13446 11326 12276  6319 11400 11828  7798
 [1229,]  2440  9144 12499  7696 11628 11182  4735  2300  6502 12107   919
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 [1250,]  3732  1402   439  3862  9591  4674  9082  2473  7791  3391  9210
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 [1258,]  7584  4946  8389  9236  1918 12003  8258  4044 10066  3888  6060
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 [1263,] 10552 10940   687  5235 12769 11064 13570  2762  9609 12426  4690
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 [1266,]  7190  7595 10618  9944  7288  6916  5113 11411  7772   794  2071
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 [1268,] 10517  3393 10305  3231  8368  6969  2576  7577  9291 10031  9611
 [1269,] 13392  4039 10842  6675 12325  5608  8211 11698 11876  6960  5801
 [1270,] 12103  2174  7363 11542  2949 10438 11583  6168 12569  4712  7196
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 [1272,]  4030 11808  5533 13056  8092 13520 11593 11036 12326 11834  1337
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 [1274,]  3184  8406 12391 10926  2960  6486 10192  5044 13441 10676  7128
 [1275,]  2206  1120  9590  2414  8166  9187  6533  9110  1489  4693  5093
 [1276,]  2176  4177  8307 10909  8243  9230  8551  7493 13560  8197  8516
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 [1278,] 12092 11212  9126  9730 11451  9657  7885   645  4388  2891   721
 [1279,]  4823  8134  2362  3845 13203  5550  2304  5610   394   938   880
 [1280,]  9327 11028 10905  9889  7922  6653  8003  7965 11999 12158  9050
 [1281,]   266    69  9099   707   128  6645  1098  1826  2470  5648   491
 [1282,]  6873  6860  7966  9836  5541  9843  8220  8804  6533  6288 13029
 [1283,] 10545 10308 13160 10857 13579 12031  7539  5777 13359 11226  9548
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 [1285,]  8179  3351 12347  2952 11111  9719  4978  3325   588  4177  7699
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 [1288,] 13575  3417  6533 11747  6188  9301 13110 11142  6172  4186  5156
 [1289,]   128  2113  3080  1402  1150  1129  1061  1871  1426  5640  2669
 [1290,]  8480 12517  7081  8530 10928  2881  7741  9597  4426  5296  2258
 [1291,] 10588  4906  3354  8260  7142  8045  3214  9430 13712  4021 10271
 [1292,] 10606  7682 13227  5200 13452 10827  7464  7224  2271  8238  6124
 [1293,]  9839  7887  7707  3013  4015 11151  3523  1603  1839  4416 13594
 [1294,]  9079  4389 10349  7515 11024 10170  5646  8426  7355  8297 11389
 [1295,]  4438 11649  6773 11774 12831 11299  3053 13584 11272 13022  7986
 [1296,]  8047  9043 10843  7969  3502  3378  6976  6262 12346  5221 10039
 [1297,]  9803 10634 10184 12911 13606 12175  5398 10925  9216  3462 13512
 [1298,]   920  5023  9479  6645  3793  3559  4057  2447 13654  2297 10706
 [1299,]  3282 13361 13300  2667  7552  1718  2902 13154  8826 10401  2005
 [1300,]  3285  2938 13509  7313 12304 11444 10778  2984 12521 13276 11141
 [1301,] 10282  4722 10836 10742 13531  9893 10750  7766  4344  3458 13054
 [1302,]  4096 13326  8362  3324  6287  3959   378  2077  1672  3230  5137
 [1303,] 11836  1641  3257  3215  7121  3911 13488  3634  7286   114 10559
 [1304,]  7074  9691 13293  9735  9174 13280 13218  5143  7776 12659  3710
 [1305,]  2173  1639  1776  9392 10824 11500  6582  4632 10156  3849  6253
 [1306,]  4965 13045  8285  3099  8963 11977 13039  8547  8180  4750  3860
 [1307,]  4446  4505  4243 10656  4518  9686 12695  7845 11054  5183  8845
 [1308,]  9784  2988 11304  3124  2973  5327 10168  8558 11198   323 10838
 [1309,]  2262  5373  1598  9529  7421  2163  1445  9033  4444 11539  7523
 [1310,]  6821 11961 11456  7472  3783  7377  7606  4241 11952 10010  6678
 [1311,]  3698  8110  2125  2216  9638 10706 13458  4785  9868 10860 12719
 [1312,]  9890 11883  5101  5088  4827 10033 11451  7557 13008  2315  9347
 [1313,] 12359  9719 11697 12104  8477  2167  8676 13001 13112  4161 10603
 [1314,]  4845  3717  1471  4852  4369   873  9067  3134  2074  8572  9837
 [1315,]  4814 10982 11532  5961  7883 10598  8042  4395 10724  1937 10993
 [1316,]  6607 11745  5091  2403  2946 11619 10890  3786 12143 13627  8209
 [1317,]  1109  9643  4496  9951  2204  6686  7920  6649  9385   323  6528
 [1318,] 12377 13085  5393 13238 10056 11499  3546  8537 10936  5879  7372
 [1319,]  6911  7810 11212  6836 13196 11299  7008 11385 10399 12480 12101
 [1320,] 10149 11675  1882  9819 12849  9694  3788  6826  4824  7705  2358
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 [1322,] 10990  8213   969  3692  5643 10727  5176  5766  3087 13253  1736
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 [1324,]  1825  7445 10637  7785  8103  8856 10703  9307  6482  1575  4769
 [1325,]  6480  7391  1234 10139  4645 12575 13384 13538  9071 10450  8189
 [1326,] 12010  9130  3597  8465  3067 12263  9406  8623  6141  5569  7280
 [1327,] 13586 12652  9835  4416  6553 12665  8791 13056  7667 12778  4572
 [1328,]   964 10031 13491 10652  3051 11761  1325 13050 12326 11919 12628
 [1329,]  6386 10612  7589  7416  6196  7086  6487  3963 13100  9387  3205
 [1330,]  9592  9819  6299 10422  6409 10361  7788 12176  5917  3528  2242
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 [1332,] 13259  8610 12304  5591  9995 13245  8385 12185  3917  9967  4988
 [1333,] 12672  7460  8732  9009  8230  8882  5850  8089 12740  4926  7835
 [1334,] 12151  6706 12355  7866 11167 12694 12693 11970  5979  6479  9882
 [1335,]  7061  5020  6601 11173 12312 11314 11331  2159 11246 10644  5845
 [1336,] 12206  9719  1378  3605  7790  5686  7109  5907  7114  6174 12059
 [1337,]  9074 10762  1512  6366  4035  6322  2711 11187  7534  4209  3474
 [1338,]   653  4807    65   787   310  1199  1625  1833  2547  2763  1173
 [1339,]   483  3360  7251 12729 10955 11539  6723 12728 13112  6220 13366
 [1340,]  8539  9884 12819 11041  6347 10230  5441  2005 11923  8358  6703
 [1341,]  9568  7948  5782  8720  6359 11001  6761  2772  5186 11477  5789
 [1342,] 13333  6112  8291 10940 10592 13564 10123 11569  7241  9679 13551
 [1343,] 10889  6544  8301 11648  8487  3873  6718  5903  8463  7507  8707
 [1344,] 12128  4369 12724  3707  3955  8659  7497 11113 11708  4406  7278
 [1345,]  5880  4253 10002 12224  2036  3546  5188  5568  3303  3987 12266
 [1346,] 11738  3499  6369  3594  2550 11380 10566  9090  1557  9467  6458
 [1347,] 12722  3151 12938  7413  1981  1495 12534  3217  4976  1051  6166
 [1348,] 10205   832  4738 10682  7213  5647 13215 12195  1789  1632  4729
 [1349,]  1783  5855   521  2660 11600  3291  6812  2553  7959  8716 10941
 [1350,]  6365  8293  2615 12810 11969 10083  9462  8237 10030 11166  6185
 [1351,]  7665  6339 10493  9289  6942 10369  2521  5043  6953  2878  2163
 [1352,]  5028  6373  8329  7417 10748 11547  9266  8076  7256  5851 10469
 [1353,] 13146  1968  7784  1545 11139  5813  3195 12656  7652  6576  7041
 [1354,]  3195  9542  8663  3128  2156  8539  9384  4221  7457  8092  7778
 [1355,]  5214  4946  5114 13431 12875 13092 11974 13349 10847  6958 10277
 [1356,] 12767 10372 10502  4039  4683  8120  9219  3649 10078 11287 10333
 [1357,] 10065 13284 12466 10547 10806 10648 11365  6291  6465  9126 13249
 [1358,]  9061  7950  1457  1136  5068 12115  7633 11249  2513  7440  4464
 [1359,]  3319 12403  2882   257  4972 11298  4831  4918  1456  2226   152
 [1360,]  8451 11133 13566 11524  5731 13089 10103 10867 11474 13086 12752
 [1361,]  4401  7651  7410  4910  6585   198 10432  7673  5495  5338  9738
 [1362,]  9590 11813  3375  5073  9866  8043  2466  5775 10936  1517  8312
 [1363,] 11851  3836  8084 12251  8016  9315  3224  1953 10010  2241 11551
 [1364,]  8887 10430 10637  7785 11390  9789  6112  7010 13144  9911 11016
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 [1366,] 10545  7176  3405  7159 12705  4905  6494  5803 12153 13125  4000
 [1367,] 12578  4266  9614  6312  6181  6131  4489  4278  5045  9206  8536
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 [1369,]  4942  8660  9875  4986  4794  8414  6582 10270  9578  8118  8042
 [1370,]  8234  1193 10888  2897   622 10649 10013 13332 10676  3631  2087
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 [1372,]   945  2679  4756  6796 12574 10688  7203  2177  2403  2697  9200
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 [1375,]  8070 10040  4558  7977  6809  6815  1693 12471  2401  8587  8145
 [1376,]  8196  7343   625 11299  7211  1288  8127  6621 10144  7130  6534
 [1377,]  8727  9946  9946 11676  9390  6227  5700  7632 11236 11970 11010
 [1378,]  9948 13581 10129  2539  6261   553 11671 10396  7979  7252 12023
 [1379,]  7532  3054 12913 11406  5813  3774 11430  6125 13199  6865 12305
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 [1381,] 11801 11892  3366  7235  4591  4816  9292  4812 13752  6818  4969
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 [1383,] 11786  6318  4873 10163  5728  4790 13675  5137  8939  7996  3897
 [1384,]  6900  7942  2064 11617  1605 11778  1328  5455  4225 11596  3450
 [1385,]  2952  4226 10729  4195  1334  9342  7322 10350  9629  1624 12619
 [1386,] 10324 11743  9185 13159  3594  4756  3253 10010  8925 11727 13583
 [1387,]  7283  1133  4322  6277  7956  6096   864  4628  8385  6919  8393
 [1388,]  4465  4637  1069  1474 12575  7681  9835  5552  8629  6464  9064
 [1389,] 12472  7350 12598 12371 12291  9929  6297  9194  9169  6807 13500
 [1390,] 11313 13443  7405 13481  9439 11084  7686 12404  6184 12482  6361
 [1391,]  7001 12703  4936  5412  6478  1701  2163   787  2700  2737  3217
 [1392,] 12270  2126  9093   660  1286  1308  1723  4520  4266  1500 11749
 [1393,]  2649  9742  8162 11568 10140  8303  5411 11111  5656  1972  6103
 [1394,] 12928 11536 13392  4428 12505 12268 12954 11200 12353 12060  7986
 [1395,]  5625  1911  8838  7718  7654 11028 11131 11907  3167 10932  6788
 [1396,] 10264 13218 10067  7078  6775  5522  3093  9893  2734  1442 12133
 [1397,]  2511 13109  1431  7825 10009 13246 11210  8782 10956  7063  9809
 [1398,]  3763  2031  2841  8973 12241  9751  9858  8897 11997 12445  5648
 [1399,]  3885  4112 10593  7430  8191  5108  9521 12994  4048 10746  1971
 [1400,]  6319 10009  4637  6577 10239  4035 13593  3682  2393 11477  9151
 [1401,]  9709 13148 11739  3231  8368 10854 10313  3045  9273  5103 12471
 [1402,] 12217 11459 12727  5727  9643  4491  3019  7803  9288  7588  7699
 [1403,] 11506 11207 12248 12485 13132  3328  8853  8067 11614  4741 13191
 [1404,]  6134 13277 13434 10217  2068 11460  4268  7535  2972  8203 12414
 [1405,] 12330 10476 13553  9195  3562 11415 13042  2708  9245  5742 12787
 [1406,]  4572 12833  7869  9481  6024 10257  8384  7573  2354  2370 10176
 [1407,] 12817  5671  4616 11131  4244  9615  6766  7629 11203 10309 11008
 [1408,]  4426  1762  4413   748  1786  3622  2402   749   170  1250  1665
 [1409,]  1139  6499 11697  6421  8461  2167 13119  6474  5014  4161 11972
 [1410,]  7204 11339 12810  6929  2996  5806  7148  4933 11406  8063  6975
 [1411,] 11175 10308  2615 12842 13139  6049 13392 10294 13624 11778 11294
 [1412,] 10269  4805  9555  3604  6762  5519  9809  4513  2176   660  9930
 [1413,] 11510 11948  8688 11736  4817 10467 12860 12256  5899 13488  3066
 [1414,]  2805 12213  1069  2962  8700  7701  4904  2147  8866  3479  5558
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 [1868,]  5760  5874  2365  5743  3466  5454  1608  1896  1388  7729 10069
 [1869,] 11937 12952 13097 12743 10238  8350 12180  8421 11839 12012  1983
 [1870,]  4584 10192 10883  1999  8528  6521  7827  9930  1212  1444  6794
 [1871,]  2649  4388  9427  5323  9538  9308 10430 11880  9442  3404  8666
 [1872,] 12909  1260  6377  5714  7781  9831  8144  7760  2890  5178  5294
 [1873,]  8430  8352  6424 13159  7959  8045 13057  4041 12085 11827 10324
 [1874,]  9065  8023 12099 10631 11758  8901 11808 11276  7576 10935 12659
 [1875,]  7121  2603  3294 10717 13065 10581  9865  3402  4964  3375  7686
 [1876,] 10617   815 12154  9443 12874  4043  5209  6247 11487  8142  8947
 [1877,] 10031  6894  8870  4922  6608  7884  2404  8111  4350 10848  5813
 [1878,] 11845 13071 10479 13602  7954  8016 12422  7317 12588 11338 11838
 [1879,]  8892 13397  3423 12900 13608 10022  9238 10127 12174 11880 11172
 [1880,] 10923 11528  3663  4430  6373  7596 13599 13257  9751 11050 13393
 [1881,] 11688 12232  3001  7834  6755  7675  6988  8957  6828 11669 12129
 [1882,]  9505  5392  5921   332 10166  2197  7478  4701  1380  6211  7265
 [1883,] 12150  6941 12020  2140 12838  5822  5074 12492  9712 12130 10158
 [1884,]  1274  7019  2524  2507  1611  3281  7831  5684  2830  7705  9777
 [1885,]  3013  8724  5143  1777 10165  2187  8488  5451  6128  7153 13121
 [1886,]  9948 11394   506  5277  5147  6947  8629 10381  2590  4115  6304
 [1887,]  1631 12421 11450 13602  1326 10210 11489  5228  8543   298  3630
 [1888,] 11394 13093 13338 11521 11314 12574 10929  8336 13667  5857 10268
 [1889,]  6963 11662  4824  1999  4336  2412  2149  2665  6607   170  2633
 [1890,]  9166  7810  2492  1053  3407  9749  9856  7295 10375  5464 12912
 [1891,]  9665 11258  8311  4017 13486 12429 13233 13179  6938  6853 11900
 [1892,]  7495 11280 12263 10916  8262 12485 11003  3183  6100  7145  9545
 [1893,]  8889 13101  6110  8814 10759  4557  9761 12606  9387  3746  5023
 [1894,]  8076 12196  7719 11216 11081  7915 13196 13341 11770  6464  5424
 [1895,]  7068  2372  2303  4755  2757  5467   706  8778    60  5750  2425
 [1896,]   628  1976  4789   693 11139   525  6191 11992  9770  4497  7044
 [1897,]  4264  8996  8831  7591 12807 10430 13604  9532 12622 13391 12496
 [1898,]  3929   916  5581  8494   770  8417   580   696  6554  4308  7868
 [1899,] 11937  3209 11733  9411 11324  4885  8378  8528  5892  9098 10448
 [1900,]  7985  3598 11532 12500  5649  6831  8203 13060  8681   550  1406
 [1901,]  5370  1301 11798  9598 12809 12971  3722  4068  2860 11649  6367
 [1902,]  5551 10818  9847  7719  5216   620  3693  1423  6358  7489  3536
 [1903,]  5528  8743  6540  1888  6337  3903  8749 10479  3065 13368  6348
 [1904,]  7066 11266  7667 10694 10776 13041 13454 10990 10182 10729  8757
 [1905,]  5167  6549  4898  6230  9274  4779  5367  5024  5536  7857  8419
 [1906,]  3895  5403  2446  5168  2238  3852  1935  1993 11045  3251 10576
 [1907,]  7129 13585  9777  8097  5482 10565  5005 10769 12415  6387  4599
 [1908,] 11564  4625  9788 10576 11692 11241  7938  6297 12340 12085 13611
 [1909,]  8208  6187  9612  2919  1423  6781  8133  5478 13752  4056  7604
 [1910,] 11348 12314 11701 12799 13425 12415  7289 13596 10978 11783 11131
 [1911,] 12953 11991  6869 10706 12341 10556  4840  6623  7893 11368  6639
 [1912,]  6409  8567 10109  4028  9848  3746  4217 12193  8931 12286 11206
 [1913,]  2728  7539 12336  2904  9227  5659  8120  9853  7016  3165 12072
 [1914,]  6560 12419 13016 13353  5837 13216 13258 11583  8073 11174  9285
 [1915,] 10347   676 10213  3078  4630  8105 11488  1994 13466  5777 11790
 [1916,]   774  2929   521    23 12366  6078  4449   845    23 12171   383
 [1917,] 12906  4504  7471  7866 12835  8711 11251 12092  4797  6437  3330
 [1918,]  9146  8883  5295  9870  8719 12383  5105 13686  5021 11531  9858
 [1919,]  9677 12454 10262  8292 10649 12003  9261 11053  5750 12244 13313
 [1920,] 13401  2332  7544 12672  4754  8154 10328  4122  2074  8111 11287
 [1921,]  2777   729  2036  4807  3860  9794 12352  2324  4280  8052  2859
 [1922,]  9604  5456 13018 11010  9284  8653  6430  7654  6201  4432 10443
 [1923,]  1080  1385  2332  1101  2621  1785  1162  8927  1932   135  2533
 [1924,]  3170  6390  7118   838  8199  5022  1368 10310 10772  9108   219
 [1925,]  9555 12903 10219  7495  5129 12861  8709  5853 12592  4273  6349
 [1926,]  1244  3906  6274 10098  1522  5325  2506  7310  8332 11322   622
 [1927,]  8730  9966  7694 12115  9466 12074  9574 12747 10469  7330  4467
 [1928,] 10540 10774  4641  7658 12087  8402  5668 12340 12306 10337 10930
 [1929,]  2857  2790 12091  5961 11778 12344   487 10998  1814  2693  2716
 [1930,] 11564  5731  9840 13390 13044  8931 10725 13659 11935 13239 10189
 [1931,] 12446  3834 12911 12885 10074  3788  8263  7495 10877   773  2965
 [1932,]  1021 11076  2473  3747 10097  1179  3870  4345   904  2867  9848
 [1933,]  6343  6020  8572 13200 12969  7135  8542  5318 13463 12272  7360
 [1934,]  6882 12865  5195  2478 13153   575 12862  7594  9266 10779  6238
 [1935,] 12986  6111  7247 10847  7947  7202 13629 10159  4908 11303 13290
 [1936,]  4632 10251 10056  3635 10506  5577  2265 13154  3276  2050  2669
 [1937,] 13395  4148 12263 13244 11925 12828  4272  7294 11682 12222  6118
 [1938,] 11692   666  3851  6808  2476   719   246  4617  9810  1492 10970
 [1939,]  1249  7764  3234 10429 12108  3207  7713  7586  6850 11023 12006
 [1940,]  5536 12564  2644  4319  5192  3897 13144 10481  7404  7416  2312
 [1941,] 11975 12812 11080  4175  8047 13134  9261  5942 10175 11240 13306
 [1942,]  8666 12904 12267   886 10926  6977  7704  8348  1134  2527 12505
 [1943,] 10446 11151 12418  8235 11274 13366 11598  9948 11178 12630 10143
 [1944,] 12606  9840  9415  9537  9485 12841 12169 10981  9320  7268 11384
 [1945,] 10497 13473 10954 12801 10611 11937 13357 12148 13169 13262  6029
 [1946,] 10261  3684  4667  2220  8782 11392  4034  4776  7172  2495   755
 [1947,]  5292 11243  9942 13228  2149  7503  3343  7315  1160   298  9137
 [1948,]  9815  8311  9602  6175  3737 12957 11618 12168 11604  8928  7292
 [1949,] 13318  8093  1018  1167  7713 12397  2404  5247  7848  5206  2029
 [1950,]  7981 12202 12064  9681 11639 11779  9704  8486  8795  4402 11041
 [1951,]  6151  1770  1748 12910  2448 10891  4522 12768 12248  7399  8665
 [1952,]  3296  3018  2026  4482   884  1874  7157  2318  5333  6945  6965
 [1953,]  9437 13473 11784 10186  5787 11993 13040  8541 13571 13092  8202
 [1954,]  9213  8200  3348   317  4296 10499  1021   521  1881  1416   254
 [1955,]  7251  6298 11682  1735  7975  9045  7357   881 13482 11196  6079
 [1956,] 13025 13054  1258  9187 11487  9563  5543  5838  5766  6806 10515
 [1957,]  3651 10536  9540  8806 11996 13246 11223 13283  4656 11929  9828
 [1958,]  1638  7665   145 10391  6313  7156  5701 10555 11053  4161  9655
 [1959,]  4302  8249  7159  7119  9949 12638 10883  9053 13527 12815 11080
 [1960,]  5791 10263 11247  3428  7589  5397   692  4559  9352  8780  1093
 [1961,]  2870  2436 12122  1566   632  7778  2212  7949  7773 12793   796
 [1962,] 13299  7962  8761 13390 11077 10677  6960 13618  6495 13369 10915
 [1963,]  8222   189  1528  6971  7215 12700  4862  8870  4320  1637  8921
 [1964,]  2854  5843  6008  5941 11789  7763  2302  4899  3565  2700  3345
 [1965,]  9755   820 10534  9459  6054  4048  3512  4193  9591 10012  2525
 [1966,] 10467  9746 11079 13470  7355 10155  5380 12272 10367  6222 10472
 [1967,] 10795  9490 11188  7787 10746 10521  4813 12579  5767 12609 10720
 [1968,]  8197  8436  6379  8992  8284  2503 11785  2120 12187  2993 11468
 [1969,]  9583  1663 12251  9277 13323 11960 13361  2077 11703 13594  9443
 [1970,]  4651  5575  4231   167  6615  1205  6915  7020   519  4700  4311
 [1971,]  4711   445  2983  2008 11874  3386 10552  5128  4401  2993  8929
 [1972,]  6332  5070  5354  7269  8012  6997 11965 11552 13199 11772 12334
 [1973,]  5321  9743  6283  5152  3067  1643  4354  6489  3926   611 13319
 [1974,]  2503  9480  5268 11717 10716 11221 10537  7725  4584  4686 11441
 [1975,]  8719  4062   987 12820  4831 11557 12018  2373 11820  2364  4629
 [1976,]  4665  9864 11847  9958  7801 13425  1663  7301  7123  2512  7614
 [1977,]  7217 10481 11633 10159  7947  3730 10881  3815  8344 11183 11173
 [1978,] 10656  5493  1786  3352  9525  3897  8663 11874 12631 10209  8717
 [1979,]  6627 10458 11983  8759  9256   477  4799  8902  2404 11823  8918
 [1980,]  4891  6518 11141  7530  6530 12009 11667 13019  5943  8288  4073
 [1981,]  9032  8032 12026 10585  8770  8940  5188 13366 13142 12705  7033
 [1982,] 11727  4784  4033  8153 11791  7739  5956 12054  3512 12156  5635
 [1983,] 12025  6442 12856 13360  6155 12999  6354 12986  5263 10001   964
 [1984,]  7978 10040  3763 10574  3356  1300  9839  7353  6400  3476   807
 [1985,]  4281  3739  1683  5485  7585  6506  3786  6861  2659  7769  3511
 [1986,]  7000 13020  3988  5411  6478  2436  8820  2612  2704  1446  1634
 [1987,] 12833  6166 11393  6638  8103  4540  7151  2951 11941  1079  2852
 [1988,]  6564 11505 11495  8479 13470 11117 12504  7388 11220  7568  3683
 [1989,]  4007 12888  7392  7586 10996  8552 13173 12772  9314 11057  6361
 [1990,]  4479  3624  3945  2862  7905 11264 11286 10200  9985  8538  7954
 [1991,] 11272  9318  5074 13581 10016 10307 13084  9113 13428 12523  8444
 [1992,]  7974  4252 12093  9755  4855  6776  8203  8873  2373  9170  5832
 [1993,] 11921 11781 12911 13001 13372  7133 12511 10291 13034 13602  8452
 [1994,]  6198  8276  7511  6068  6942  1426  4228  4628  6953  9689  2148
 [1995,] 10634  5671  8875 11127  6528  8412 10390  2964 12321 12695  6921
 [1996,]  3661  7584 10813  9949 11935 11897 13217 13201  9837 10734  5806
 [1997,]  4417  9985 11440 11153 11046  5179 10400  4948  2361 12963  5888
 [1998,] 11921  2329 11716  4018 12902 10155  7316  3764 10310 11239  7240
 [1999,]  6346 13045 12641 13497 12367 13312  8549  3780  6929 11805  5031
         [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22]
    [1,]  6382   582 10318  1026  2826  4493  4201  4927  5573  2019  3881
    [2,]  7327  7151  7293 11570  4016  9587  6367  7952 13494  2125 12990
    [3,]  7731  8213  1510 10081  4012  5151  4245 12918  4055  7988  6427
    [4,]  1591  1915   121  2302  4587  3873  7282  2904 10325  7092  5541
    [5,] 10395 11267  5356  3707  5636  7008  5096  6344  1472 12122 11079
    [6,] 10759 12352 12780  3741   900 11992  8173  2570 10890  2754  5904
    [7,]  8097  9136 12398  2450  7459   901  8341  6951  8674 10336  1134
    [8,] 10809 11621   408  9254  6786  2783  6385  8206 10995  3033  8742
    [9,] 10291  4940  7732  8219 11518  4330  5063 10747 11084  5942  8860
   [10,] 13408  2054  3674  9816  4999  3684  3306  4838  9263  7944  5188
   [11,]  1880   823  2247  1883  3553  1135  4497  1551  7025  4129  2515
   [12,] 13328 10199  6849  3431  9516  2005  8511  5247  2466 10791  8895
   [13,]  3244 12390 11070  3041  8196 12747  9867  8255  7797  7697 10272
   [14,]  3268   594  2139  3128  1031  3694  2459   667  1818  1534  1304
   [15,]  8436 10744  6146 10380 11125 12026  8459 13144  8020 10731  8503
   [16,] 10384 11485 11620 12924  8063 13325 11946 11548 13361 10207 13622
   [17,]   453  2838   633  2396   555   773  6417  1485  1492  1315  1558
   [18,]  3455  6701  3214 12422  1081  3064  6701  2251  4198  8226  5572
   [19,]  4103  6347  2331  4874  8178  9744  8744 11291  9854   400 10261
   [20,] 12555  7518  5145 12288 12970  1409  2735 12578  6771  6784  5148
   [21,]  8891  2705  9002   316  6514  4950 11865  9096  3355  6202  3423
   [22,] 10540  9129 11068  4008 12431  9638  9911 10450 12445 12668 11024
   [23,]  7699  7917 13039  2436  7577 12749  3587  8066 13395  9722 13168
   [24,]  5844  7615  6813  7657 10795  7317  2507  7417  4819  4057  1400
   [25,]  4325  4598  1419 12776  3664 10607 10064  5726 12177 12428 11341
   [26,]  8908  4148  4790  8562 12552  8060  3635  4225  5196  9275  1966
   [27,] 13043  3792 11258  5876 11459  8766  8746 11045  7938 11763 12342
   [28,] 12282  1536  5294 10117  4246  6314  2559  9158 13403 11370 10378
   [29,] 10891  9045  3314 13672  9833  5205 11894  9455 11165 10307  4521
   [30,]  3641  4006  5481  5963 11526  4167  9502  8483  8542 13266  8026
   [31,] 11510  8868  5189  4417 10466 10118  9279  4866 10192  7133  4222
   [32,]  3410  5766  6202 10081  2344 10152  7152  6721  9403  8175 12099
   [33,]  6553  3987 11095 13257 11093  6545 11724  6354  9919  9791  8443
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   [35,]  8796 13461 10498  9611 12968 13050 12164  9622  3873  8142  8789
   [36,] 10774  5631  2233  5296  6766  3183  1208  8326  3746  9833  5145
   [37,] 13217 11657 10441 12229  3260 13088 10699  9109 12095 11910 10409
   [38,] 12420 12108  5267  2217  4933  3607  5172 12848 12472  7686  3580
   [39,]   551  4968  9817  5412  3735  8950 11830  3279  9296 12792  3371
   [40,] 11496 11973 13180 11690 13650 11472 11292  2790 13410 10648 11901
   [41,]  5271  7276  9259  9034  3190  7860  8086  4352 11609  2170  6409
   [42,] 11074  6252 11097  5176  9730  1872  8299 11578  4657 10665  6126
   [43,] 12272  5897 12647  4311  8601  2424  4403 12611  9640  6428  4997
   [44,] 10797 13461 12986 10249 11144 10943  8478  9852 12966 12495  5248
   [45,]  2801   956  1397 12693   147  4136 10697  9109  7572  1894  2241
   [46,]  4373  9029  9689 12266  8783  1158   884  7955  4689  9808 10326
   [47,]  7680 13108  4675 10232 11677  9661  8472  5248 10970  7048 12439
   [48,]  4748 10385  6958  8508  3356  2578 10872   954 12299  2401  2593
   [49,]  7789  8990  9381  1747  8663 12792  8462  8241  9368  9128  3352
   [50,] 12125  4167   607  1803   683 10735  9469  2227  4213 12094  4357
   [51,]  2441  2876 11623 11476  2954  7772  5114  4748 11435  3640  7953
   [52,]  3322  8804 12586  3614  9126  6144  7111  5886 11703  5097  7082
   [53,] 11922  9616  4961  9940  8284 10632  5002 13222  5029  7005  5232
   [54,]  6959 12307 13016 13183 13219 12353 12259 13433 13225   388  3657
   [55,]   750  4154  8032  1790  4903   648 10846  5179  7312  9253   650
   [56,] 12304  6578  6990  8598  2197  9109  6929 13260 11592  3072  3187
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   [59,]  6062  6420  3237 12137  6998  6396 11658  8962  6587  9645  8217
   [60,]  2241  2425  6065  9953  4783  7345  2241  1877  1408  2551   989
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   [62,] 11284  9425  7734  8188 12887 11347  9853 12536  3998  4910  6390
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   [64,]  7823  5188  1286  6581  1822  5814    52  2125  1022 12516   412
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   [69,] 10633  4648  8323  7790 13646 13226 13095 11478  2738  9478 12418
   [70,] 13068  9561 12259  9917 13513  3446  6225  9122 12479 11304  4622
   [71,] 11335  3538  4965  6177  5651  2931  9047  9345  7169  8055  7546
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   [73,]  7218  3845 12021 10665 10024 12812  8862  9435  5511 11271  2717
   [74,]  7525  4127  7732  6197  5170  2784  1589 13052  1712   440  9681
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   [76,] 11267  5911  8133 10740  9025 11170  4941  8963  1445  5315  9931
   [77,]  8340  1643  5163  8163  1131  1151  4948  7020 10023  4585 10223
   [78,]  6666  9628 11480  1183  6568  6884  5557  7137  2445 11470  6675
   [79,]  3773  4503  5005  9484  6412  9332  8265 10766  2702 11706  6032
   [80,]  4833 11740 12517  8742  8905  7504 10310  9695  8524  8305 12191
   [81,] 11709  6981  5931  3007 13043 10386  2999  9727 11225  5227  7931
   [82,] 13440 11367  9429 13142  6661  9388 11833 13420  7105  1683  3371
   [83,] 11327  8517  2370 12608  1935  4582  6198  8853  5528 11822  9977
   [84,]  8426  1710  7890  2633  7449  7233  1909 11742  8017  5723  3069
   [85,] 10278  6940  3996 13609  7449  7423  6449  5538  8916  7739 12841
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   [87,] 12630  9927  9142  7678  5204  8168 11575  3640  8184  1608  6333
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   [95,] 12243  8985 11893  3371  3335 11964 12668 12743 12637 10859  9756
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  [319,]  2014  6914 10302  5819 10578 12843  7777 11165 13032  8539  1406
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 [1367,]  1011 12632  4006  9121  9048  6481  9913 12417 12000 11259  9271
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 [1410,]  4163  8716 13430  2797  6111  8172  9880   839  1280  7081  3206
 [1411,] 10966 13356 12956 11883 10683 10329 10400  7916 12112  7583 10220
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 [1416,]  6516   782  5047  5737  5506  3182  5469  2588  3818   415   270
 [1417,]  9220 12622  8241  5208  4853  6338  9117  1977 11942  5422  7104
 [1418,]  3553  6584  2663  7811  2014  2970  6423  6369  5763  3699  6085
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 [1422,]  9108  4782 10589 11279 12985 12524  6793  3349 13033 13398  7975
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 [1427,]  2602  9493   295 10274  5601 11913  5665  3254  3322  7204 13245
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 [1429,]  4295  7168  9806 12179  5557  9917  6301 12557  6013  6914  5340
 [1430,]  6174 11613  6851  8344  7431  9582  3447  5017  7230  2950   844
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 [1432,]  3217 10417 11865  9846  9038 12582  7056  9815  9775  6564  5697
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 [1435,]  7504 12347  5895 12604  5012  5973  5217 12680  9275  3761 11954
 [1436,] 13519 11128 10054 12207 11568 13341 10559  9123 13548 11859  9261
 [1437,]  9828  2531  7924 12829  6566 10230 13137  8650  7116  6050  7658
 [1438,]  6856  6755 10296 11760  7414  1541  9456 10821 10387 12847  9868
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 [1441,]  3840 10546  4396  4939 12501  1325 12000 10397  3849  2848  2363
 [1442,]  4165  2414  1263  3970  3003  5786  7168  1085  9426  3902  1971
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 [1893,] 11027 13291  8617 11811 13076 10079  3899 11179 10115 12059 12923
 [1894,]  9795 12170  9720 13028 11044  8932 12383  8636 12172 10038  5329
 [1895,]   243  2057   369  5060  2971  2435  2290  5657  3213  5794  2610
 [1896,]  6895  3560  6176 12844  7808  5131   830  1571  3984  6092 10628
 [1897,] 12510  3461 13357  6452 13318 10943  3520 13003 13137 12391 10360
 [1898,]  8986  6164  5700 12692  5763 12620 10649 12268 11452  5660  2348
 [1899,]  6425  7991  8194 10742  8868 10501  8055  9884  8691  9418  7948
 [1900,] 13440 13407   563  7478   953  5678  1357 11699 12207  5816  3265
 [1901,]  3511  4649  8913  7693  7539 10234  4387  7324  3463  7515 11857
 [1902,]  9777 10255  3717  6405  8569   936  9315 12652  9899  2773  7425
 [1903,]  7310 11203  8308 12753  7469  3419 12447  7965  9984 10680 12445
 [1904,] 12410  3631  9612 12633  9244  8196  7173  7550 10321 10820 11982
 [1905,]  6059  5901  4231  3974  8032  4192  6001 12884 13067  7619  2865
 [1906,]  9391  3712  7225  9131  7907  8460  6274 11916  2016  8483  7112
 [1907,]  3396  6184 12057  8321  8402  7921  9875  5269  7289  9095  6443
 [1908,] 10675 12734 12673 10202 11165 13395 12457 12923 12942  9016  6537
 [1909,]  9578 13149  5178  3951 10935  3690  2335 10190  9393  5924  7505
 [1910,] 12157 10849 12736 11311  9855 12538 13180 10540 11215  8306  9121
 [1911,] 11330 11582  7637 12094  9236 13365  9929  3911 10339  4775 12094
 [1912,]  4091  8018  8534  4875 11873  3571  5895 13551  9736 12909 10890
 [1913,]  7245  6028  8465  6087 12041   879  7171 11627  5089  2108  3442
 [1914,]  7191 12301 11773  4611 13613 12357 13050 12719 13344 12891 10812
 [1915,]  5885  4730 12745  3805  7890 11036 10884  9758  7687  6520  9989
 [1916,]  4621   556  4206  7827 11236   765  7725   709   225  6305   628
 [1917,]  8462   977  9721 11727  7578 11870 12994  7433  8267  3040  8770
 [1918,] 12660  6053 11987 10059  8291  4350 11171  3805  9200  9077  2462
 [1919,]  2187  8765 12043  7946  9904 11686  3900  8958 11894 13132  5677
 [1920,] 13298 10404  2344  8086   700  6587  9794  7695 11943 11272  2860
 [1921,]  1197  1131  8091  8963  3969  5736  3149  4329  3236  2094  3466
 [1922,] 13225  9892  9317  1092 11574  7262 13081  8163 11974 10540  4826
 [1923,]   884  1017  1372   675  1660  2013   127  1014  1297  2986  4453
 [1924,]  9657  9141  5265 11488  4588   613  7239  5631  1548  3610  8254
 [1925,]  2829  5049  8819  5297  5363  6308  7400 12223  5596 10601 12835
 [1926,]  6270  6501 10997  2006  7996  7018  5099  8479  3414  9297  1409
 [1927,]  7913  3808  5642 11597   806  9780  5266  3587 10569 11688  2337
 [1928,] 11982  4518  4638 10972 12642 12398  4450 11575  9982 12372 10332
 [1929,]  8036  9746  6898  7817  8802  3134 11372  8648  5128 11552  8801
 [1930,]  7801 13456  8366 13335 12616 10961 13245 10797 10240  4118 13683
 [1931,] 12339  6978  2465  9658 11397 10501 10289 10915  2028  7302  9131
 [1932,]  3845  8179  2103  2170 12846  1230  3102 11441  1743  2859  1285
 [1933,] 13188 11115  7018 12548 12765 12864  7847  6771  4401  6322 13059
 [1934,]  8328  2081  3645  7096 12474  9560  8076  4748  6680  7714  5891
 [1935,] 12722  8080 11024 13171  5857 10504 10358 11104  4431  9347 12705
 [1936,]  7856  4705 12712   908 10456 12778 10204 10513   583 10980 13428
 [1937,]  8340 11570 12843 12108 13572 11696  8895 13504 13256 13575 10979
 [1938,] 10034   326  1146   491  5788  1578   983  1233  2536  7244  8566
 [1939,]  2810  8785  8928  3589  3309  6050  4425  9051  5420  4460  7369
 [1940,]  9444  4251  9198 12748 10302 10453 11312  3568 12919 12765 11838
 [1941,]  9317  7003 13168  5075  6957 11112  9811  6230 11938 11240   362
 [1942,]  1431  5723 13283  7453  6429  1238 10687 11749  2655 10398 10405
 [1943,] 13241  4614  7133  7864  9754 12705 13161 13444  4304  3346  9097
 [1944,] 11494  4836 11665  6371 13320  5639 11239 11146 11483 13206 11101
 [1945,]  3663  4782  4365  9653  9879  6361 13167 13603 12763 12620 11506
 [1946,]  3425  4995 10803  1194  5527  9882   865  7850  4103  2913  7828
 [1947,]  6333  3578  6029  1960  3891  7098  6889  5434  6398  3458  3845
 [1948,] 12597  8653 13414 13188  9929 12996  7792  6532  1562 12947 10223
 [1949,] 12079  1153  7296 11591  8276  5153  8322  4432 12694  6918  1309
 [1950,] 12902 12450 10032 11187  8749 12450  1839  8876  8029 11966  4075
 [1951,]  3051 11656  8807  5283  9457  3392  4329   942  2865 11340  9415
 [1952,]  3194  7528  1199  1506  4578  7888  1727   819  4948  6856  3200
 [1953,] 11640  3736  9886 13354  7984 11648  9514 10696  5525 12552  6866
 [1954,]   277 11075  2290  1230  1228    52  2080  4079   581  3210   281
 [1955,]  9111  9287 11829  3801 11539 12087 11109  8774 10421  8311 10866
 [1956,]  5972  4632  6689  3598  3154  1006  6892  9472 10890 12270  5947
 [1957,] 11262 12110  7634  6194 10132 11847 12375 12767  6080  9081 10571
 [1958,]  5444  2379 11448 12712  8665  5435 13297   352  5447 10356 11179
 [1959,]  8135 11845  9490  1499  8117 11916  3828  7401  6555  7664  4689
 [1960,]  1346 12736 11918  1974  7621  4064  1431  1926  2994  5196  4983
 [1961,]   825  1939  9031  1958  3076  1053  2782  8250  3302  3240  8924
 [1962,]  8823 11344  9697 10044 12573  6147 12383  9073 11036 11990 10624
 [1963,]  5237  7809  4414  9844  2724  1017  7282  2243  3242  4792  4507
 [1964,]  6897  7969  1944  5792  4040  1552  3465  7540 11099 10097  9875
 [1965,]  9604  5956   453  4008  4976  1392  2172  3682  8687  1870  7150
 [1966,] 11955 12012  7739  9162  4864 11191 12377  4506 13097  8649 12322
 [1967,] 13591 12992 10355  6018 10083  3770 12319  5117   513   973  2358
 [1968,]  7147 12120  9570 12065 13275 11287  5033  3060  5058  2859 12080
 [1969,] 10884  9096  3568 10487 11264  5206 11075  9377  8591 10985  5601
 [1970,]  6097  9215  6720  3103  1403  1154  3313  1648 12257   436  5286
 [1971,]  2342 12516  1935  2177  3948 11288  9093 12283  3843  9917 12491
 [1972,] 10118  3207  9046 12899 10629  6360 12908 12966  6309 11668  7972
 [1973,]   463  4468  4526  1664  4866  3956  4124  6956  3547 11683  3687
 [1974,] 12153 12509  5412 10605 11466  9416  6917 13517 12130 11419  9579
 [1975,]  6325  1632  9320 12923 13396  6705  5772 13152 11261  4405 10112
 [1976,]  4994  2183   281  4170  4323  1294  4361  9521  2441  8086  4207
 [1977,]  7154  3768  2048  6914 12367 10986  9730 11101  8597 10315  8129
 [1978,] 12058  6403  6124 12164  9492  9712 11708  3660 11884  4480 10358
 [1979,]  2346 13019 12836  6651  4952  4818  5881 12994  6934   280  5176
 [1980,]  5620  4804 12666  5307  9550  5636  6429  8100  8952  8807  3928
 [1981,]  2584 11618 12983 12782  5738  7942  1348  2615  8236  2924 13219
 [1982,]  9058 11104  8575  5519 11585 10740  8619  7573 10403 11575  7709
 [1983,]  3153 12396  7085  4715  7104  5906  5199 10237 11569  3587  3881
 [1984,] 12094 10761 11163  8316 13543  3968   155  8654 10271  9110  4276
 [1985,]  6787  5215   992 10309  7422  3704  4662  1583 12568  5155  9408
 [1986,] 10370  9008  1006   856  2436  4938  9438  1003  3830 10974  1090
 [1987,]  5176  6447  4979  6001  1336  7891  5179 10550  5960  1458 13633
 [1988,]  9704 11956 13510 11168 13293 13391  9010  6642  6540  8528  2134
 [1989,] 10339  8942  8897  9545  3324  3941  1244  4631  6874  6798 10378
 [1990,]  5682  2186  2662 10996  9742  7938  2747 10497 11642  7050  7685
 [1991,]  8155 13451 11243 11210  9925  5858  9552 12673 12327 11623 12227
 [1992,] 12374  3860   346  8070 10135  9903  6070  9311  8135  7955  8638
 [1993,] 13183  8050 12914 12454 13367 11682 13056  8975 12777 11180 13725
 [1994,]  1474  1590 13415  6859 11197  6391  6740  4242  7443  7351  9989
 [1995,] 13148  6413  6100  9290  2642  5629  4475  3448  2646 10396  9550
 [1996,] 11928  8726 11812  3151  3949 10097  6246  1280 11773 12444 11327
 [1997,]  2672  8256  3158  4301  2030  6735 10817  6690 11529   614  9557
 [1998,]  8279  5970 11279 11900 13370  6490  8161 13442  9804 11156 11517
 [1999,] 12909 10005 11755 13375 10677  9498  9552 13442  7658 12641 13051
         [,23] [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33]
    [1,]  3069  3580 11012 10545  3059  7699  1767   427 12925  8945  4821
    [2,]  4193  2338 12108 13154  4185 10231 11682  8413  6691  1898 12591
    [3,] 11157  6087  3469 12602  9624 12581  7891  9566 11223  3313  6337
    [4,]  4044  6096  1092  2443  2802  2141 11657  2294  8016  1878  5326
    [5,]  6728  1087  4109  7055  4004  2950 11818 10023  2809  2167  2238
    [6,]  1871  3796  9558  2042  7856 11780 12434 11458  8891  4818 10122
    [7,]  1925  9079  7841  6507  2634  8855 13119  6954  2066  3757  8051
    [8,] 12344  4168  8622  9440  8302  6968   563  6629 11950 12366  7472
    [9,]  4184 12386 13467 11864  8633 11359  9130 12093 12749  9123  1705
   [10,]  8639  3207  2278  7538  2111 12128  6688 10920  8004  1863  6397
   [11,]  3597  1790  2588  7883  1676  7135 10869  7597  1639  6784   352
   [12,]  2871  9506  5399 13372  1779 13300  7043 10441  6948  5485  3268
   [13,]  1179  4978 10989 11306  2269  5772  8635 12517  8984  5092  2837
   [14,]  9588  6146  1833  1271   696  1626  1471  4332 11230  2019  8649
   [15,]  7365 11275 10155  9316 12017  7234  6544  8396  7741  6094  7237
   [16,] 13550 12104 10582 13132 13456 12062 11865 10032  7222 11134  9835
   [17,]   986  3611  1152  4157  4465  6063  3932  1359  1459  8465   232
   [18,]  1075 13433  4397  7816  1616  1920  1012 11215  3482  1608  2500
   [19,]  7699 11787 13616  5891  8807  9403  9564  7400 11480  4973  7074
   [20,]  6592  6331 10389 10607 10036 12958  7719  7736  8975 12366  6045
   [21,]  7414 13432  5034    53  4429  4420   892 11223 12486  4413  4463
   [22,]  6896 12946 13117  5893  8743  5750 12433 11456 11707  6573 13012
   [23,]  6377 10131  2565 10595 10589  3317 10619  8702  9738 11997  5775
   [24,]  8862  2296 11565  5051  4189  5051 12160  8339 11761  4249  7689
   [25,]  9745 12794 12557   777  7246  7148 12596 11614  9242 10061 10992
   [26,]   754  6427  5473 12901  5439 12738 10960 11190  3420  8085  5498
   [27,]  8608  7566  6170  9677  5049  6743  1032  9203 10056  8866  1443
   [28,]  6110  5773  2828  6328  3571 12622 13320  5689  2120  2782 13452
   [29,] 10016 12064 11831  9990 11508  8329 12732 13507 13561 11743  8716
   [30,] 12197  8774  7791 12045 10258  3616  8492 11255  1863 13191 11390
   [31,] 11638  4870 11115  3425  4482 10349  2825 10447  5624  9607  3329
   [32,]  1906  7186  8287 10962  2182  5004 10948  6334  9215 13321  5368
   [33,]  8193  3506  9854  6892 11285  3317 11415  2690  9735  9893  6797
   [34,] 11465 11787 12591 12978  7034  4819  6432  9466 10680  2400   996
   [35,] 10524 13594  9273  7367  9062 12379 12199  8745  6776 10108  8540
   [36,]  7494  9403  1897  2635  4499  8814  7705  1252 11725  9599  7118
   [37,] 12932  3511  8897  3222 10571  8085  7689  6780  6363  9949 11943
   [38,]  5909 10112 12211  9407  1549  2995 10550 12150  6176 11858  3755
   [39,]  8464 10484  6390  9351  6164  9653 12213  8739  1649 10935   334
   [40,] 11197  6862 11192  9801  9987 11929 13460 10109  2774 13525  3941
   [41,]  6960 11114 11708  3905 12740  2236  6738 11051  5541  8607  4199
   [42,]  6084  8419 11627  7617  3352 11763  1774 10237  8944 10114 13229
   [43,]  8963  5625  9777 13356  3201  1725  8357  4729 12677  9876  5598
   [44,] 11193  7436  6501  5165  3388 10972  8009 13102 11909 13383 11169
   [45,]  5257   218  1455  6307  3377  2461  2947  2687  7624  5339  4777
   [46,]  4470  1397  5067  1904  9733 10281  1541  5980  9985  2247 10640
   [47,]  9785  9439  7606 12221  9902 10343 13499 11695  3267 11621 12174
   [48,]  7437  9624  3172  8886 10717  7291  2154  5559  8274  1986  4302
   [49,]  8238  6289  7206  3334  3358 12714  4607  4159 12730  3376  8530
   [50,] 10637  7543  6531  6354   715  8200   567   533  1155  2081   853
   [51,] 10303  9150 13120  5463 11185  6729 11371  9535 10764  8191  2074
   [52,]  6194  8251  5351 11942  7842  4028  7843  5338  8107  1540  6399
   [53,]  4994  8333 12213  4386  1598 11740  9076 11642 11183 10895 13524
   [54,] 11300 12105 13022 13037 10959  6433 13612 13289 13287 11079 11492
   [55,]  5154   309  1691  3097   811  3396  3613  4520  3424  5618  6533
   [56,] 13384  3025 13076  9234 11751  6488 13365  6303  4234  5916  3411
   [57,]  8020 11630  2825  7375  7063  7855 11821  8860 11564  8850  5711
   [58,]  5327 13403  6369 11696  9763 11419  5631  8663  4460  8011 10258
   [59,] 10330  1386  4723 12923  4754  3134  7521  4716 12599  4014  7920
   [60,]  5057  1034   736   613   210  2373  4040  6794  1429  6914   618
   [61,]  8473  1903  3556 11987  2592   413  1257   528   196  1164  3826
   [62,]  2362  4091  3072  9659 13495  3742  6731 12838 11818  4792  6438
   [63,]  1889   567  5020  8380   811  1906   864  2635   479  3288  1732
   [64,]  2483 10532    78  8855  1228  5344  1826  1035  9451  1769  2738
   [65,] 11193  8546 12954 10990 10035 10383  8769 13254  6116 13610  7160
   [66,] 13690 10784 13575 12081 12220 12090 12420 13180  9575 13000 10852
   [67,] 11194  5158  5344  8794 11468  4028 12958  7723 12797 12364  8701
   [68,]  1213  6033  1251  4954  2132   493  1878  4202   439  2864  5243
   [69,] 11991 12254  8469 10593  4343  6234 13122 13011 11591  8805 10943
   [70,]  7920  3040  4927 12969 12314  8491 12031  4128 10768 12543 12447
   [71,]  5990  8236  7314  9709  2248  6734  2067 11053  1084  8016 12171
   [72,]  8202  6231  2425 12359  9872 10965  7898  3104 10176  6695  8529
   [73,] 12256  3031 10662  2129  7681  7533  6415  3998 12873 13119  8966
   [74,]  6011  6122  6295  7652  3148  2272  2035  6460  9350  5032 11783
   [75,]  8071  5606 11446  6410  5906  5050 11212 10060  2153  5987  5009
   [76,]  7887   603  2040 11785  7826  5555  6014  5957  9505  6511 11326
   [77,]  1198 11122  5070  7861  5826 10001  6399  4035  9907  9208 10648
   [78,]  5326 12416  4943  4306  3248  9659  5880  5108  3205  4596  3236
   [79,]  9658  6717  8032  9537  6124  7861 11126  6920  2691  6545  2967
   [80,] 13414  9765 10591  8059  9366  2004 10295 10653  7552 11912 10490
   [81,]  4862  8883 10520 13683  4726  6396  9365  7929  8428  3501  6769
   [82,] 12006  8531  9553  6799  8004  9672  8065  7597  6864 11612 11203
   [83,]  8740  6857  7362  2804 13469  6712 11919  7028  7376 11798  9866
   [84,] 12935  5645  4805  1984  6117 11396  7680  2011  6300 10657 12113
   [85,]  8145   955  7888   592  2500  4129  2284  2049  3929  4011  5905
   [86,]  7437  8578  3153   858 10718  9100  1010  8836  4624  8492  8614
   [87,] 13128 13159 10832  5650 10253 13358  9845  9272  1537  5920  4419
   [88,]  1018  6396  5442 10655  3468  8194  9809  5535   515  5444  1110
   [89,] 11984 13190  4361  7370  9056 13179 13399 11752  9361 11661 12587
   [90,] 12435  6571 11233 13201 10843  8311 12373 11856 12529  6486  9658
   [91,] 11357  5945  8088 10142 10232 12122 13363  9212  4186  1537  4036
   [92,]  7032  2286 10090  6480  3802  4912  2654 10965 10310  1133  2299
   [93,]  2317 11407 12759  6875  1357  7538 12863 11280 12901  6559 12716
   [94,]  5337   813  9264  7296  2632  2447  7040  5408 11156  6149  4255
   [95,]  7197 12436 11586  4012  9796  2467 12620  9351 10257  5506  2293
   [96,] 13102 12886  8802 13671 12116 13404 11853  3732  2966  8828  7991
   [97,] 11034 10467 11611  9657 13365 12959 10602  7285  5097  6094 12807
   [98,]  5333 12412  1117 13253  9045  9683 13197  5385 10167 11569  9389
   [99,]  3607  5239  1864  6213   796  1711  9775 11127  9740  6639  7246
  [100,]  6682  2713  7698 11767 12557 12088 12310  2778 10560  2582 11334
  [101,]  6369 11262 12241 11386 10535  6147 13396  7616 10425 10033  3246
  [102,] 12682  1241  5269  4091  8907  5197 11614  7684  8750  5568  3336
  [103,] 13644 10759  8006 12472  7603 12423 11063  9895  9720 11380 10820
  [104,]  2800  3456  8677   867  3446  2680  6852  4572  3542  2392   915
  [105,]  4380 10399  6809  1378  8377   865  2443  5091  4985  8481 13366
  [106,]  9527  3188  9077  9608  8548  5672  8845  9278  1538  5710  7365
  [107,]  1995  7529  7243  1649  1914  1949  3844 10550  3530  8459   221
  [108,]  3918  2042 10605  6876  8610  6560  8264 13489  9600  1794 10502
  [109,] 13278  5816  1607  2487  9609 13462 12136  5333 11741  3560  6433
  [110,]  9785 13326  9261 12885 12371 13154 13682 13505 11775  4268 13118
  [111,]   656   846  2246  2017  7360  5387  3423  2175  2576  4235  1610
  [112,]  6579  3706 11197 10619  7292  8984 12088  8703  7786 12799 11487
  [113,]  4924  1356  7708  2397 10339  8455  4898  7839  4949  2937  4603
  [114,]  5419  1815  7902  6741  7322  4363  4386 13264  3447  1761   637
  [115,] 12689  5123 10403 11350 12842  6999 10028  8630 12441  9606 11791
  [116,]  8048  7907  6936  4268  7080  5965  4035  2863  3998  4502  8298
  [117,]  4518  7987 11150  9735 10829  5136  4353 10477  9877  1378  3049
  [118,]  6166 11877  7184 12005  9001  6043  3783 10286  5492  1926  3456
  [119,]  2374   439  3295 11383  2202  9421  7981  9472 11933  5009  7615
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  [854,] 11331  3187 10043  2903  4681  4511  4759  9244  9084 10872  3407
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  [873,] 13621 11644 12988 12111  8442 11028 13526  9014 13379  4123 12958
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  [875,]  7668  6765 12176 11595 13701 10059 13536  3801  6511 13546  8736
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  [890,]   996  6368   764 11730  4554  8255 13012 13125  7001 11208  6546
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  [893,] 12783  9323 13071 12175 12933   687 10894 12054 12316 10016  3115
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  [903,] 12058 10644  7791 11442 12533  6530 11729 13146  4752  1645 12750
  [904,]  6842  5075  4182  5568  1074  2282  2114 12139  6964  3862  8649
  [905,]  3420  2345  4929 12004  9756 10321  9143  1697  4301  5816 10441
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  [907,] 10431  2296 10141  8341 12761  7035  8590  9376  9881 10437  8276
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  [910,] 13035  5534  6791 12491  4653  7357  6129 10685  2965  4618 12676
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  [913,] 10674   634 11362 13471 13164  2745  9582  7168 13094 13449 11849
  [914,] 13396  5668  4715 12515  6823 11098  6382 10649 11629 12074 12336
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  [917,]   480 10461 11140 12428 12370 11420  5881  8672 13601  3878  4237
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  [926,] 11476 13258 10666 13577  4649  5607  3123 12614  3965 12862  7835
  [927,] 12771 13504 13343  9021 13681 13196  7235 11262  8517  1647 11269
  [928,] 13375 12076  9685 12531 13156  7440 13041  5726  1851 12997  5572
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  [932,]  3111  7082  2133  3215 12748  1066  7616  7208  4088 12873  8019
  [933,]  7973  9690  6829  7487 13686  9464 12319  3746  6413  9221  2015
  [934,]  9684  2464 11611  1809 11244  9661  5665  7307  5511  2482  8373
  [935,]  5039  6417  1614  2950   710  1949  1494   858  3496  1251   203
  [936,]  5219 13557 11593  9416 10555 11403 10072 12802  9229  1568  6495
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  [938,]  6837  8026  5900 11213 10882  7587 11511  5050 10988  4285  5114
  [939,] 10719  5833  3022  5259  6677  8407  9821  9248 10982  3559  6268
  [940,]  6746  4020  3232  7026 12758  2951  6364 10319 11683  6586  5958
  [941,] 11024 13534 11600  2252  2734  6201 11588 11609 11776  8454  5133
  [942,] 12239  3764 13544  5954 13440 10046  1678 12720  8638  6586  5025
  [943,]  9920 11965  6506  7369  5354 12976  8061  8723 10346 13436  7526
  [944,] 11997 12429  9528  8422 12455  9691   905 11715 10361 11256  7404
  [945,]  2001  9667  6136  3137  6553  7337  7971 12907  1808  7306 10456
  [946,]    61  4556  9943  9105  5714  9289 11052 11298   892 11692 10072
  [947,]  1665  7736 13570   533 10241  5418 10293  4653  5964  1647 12065
  [948,] 10934  8318  8440  5567  8695  5854  8103  8586 12462  3651  2404
  [949,] 12688 12476  5278  7703  8924  8908  6962  5493  1105 12178 10426
  [950,] 13656  6655 10970  5948 12268  6670 13096 12720  9521  7728 12840
  [951,]  1756  8569   154  3271  1107  2661   524  8816  1740   282  1312
  [952,]  2569  6378 12667 10246  3450  6318 13404  9716  3418  1755  8606
  [953,] 10208 12690  9818  7138 11581  9322  4240  5028  7590  6388 10678
  [954,] 10238  5546  9364 12719  6074  7687 12875  2205  7766  7378  9106
  [955,]  3323  2319 10337  5098 13503 12625 13197 13087 12429 11581 13110
  [956,]  6087 12857  8833  5315  2354  6803  4920  5738  2646  1097 11926
  [957,]  4914   986 12907  6564  3097  5805  1594  3928  2820  7451  3772
  [958,]  4683  1946 10591  4613  4644  5419  9204  7866  7243  4000  7780
  [959,] 11933  2370  2166  8629  4767  5890  8666  1161  5140 11818 12016
  [960,]  9571  5986 12421 12857 12636 12131 11348  7241 11490 10287 12713
  [961,] 13445  3719  6144  9016 11069 13488  2305  9811 10837 10647 10053
  [962,] 10877  9351  8090  6129  7599 12108  9873 13026  1041  7203  5088
  [963,]  6279  2040   974  1374  7093 11389 13253  2123  7082 12046  4497
  [964,] 12804  2253 12502 11201  4684  8399  6639  4982  6625  5695   569
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  [966,]  4875  4487  4512 12012 12201 11685  7186  8984 11389  7170 13041
  [967,]  5107  2528  3750  3066  2545  8219 12563  6675  4554   970   979
  [968,]  8638 12383  9122 12197 10412  3582  6967  9244  7970  6794  5506
  [969,] 12473  9851 12461 11116 11626  8356  9373 12966 10889 13288 11550
  [970,]  5551  3392  7641 11720  5523 12986  2838  1284  4597 12377  9618
  [971,] 10469 12508  7815  5761  4278 12357 11744 12424  6431 12777  4504
  [972,]  2912  5834  2452  6121  2096  2951  3466  4265   374  3611  3191
  [973,] 13414 11467  6662 10818 13530  8381 13533 12323  8459  6489 11844
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  [977,] 11465  4017  7335  6064  6048  7692 13160  6362  7764 12238  7080
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  [979,]  7559  6975  8596  7359  4575  2533  1158  4425  8764 10531  3996
  [980,] 11049  7896 11715  5923  8855 11854 11893 11481 11551  3084  2632
  [981,]  8931  7995  3856 12841 10652   828  2427  2061  7510  6457 10126
  [982,]  5945  2657  4709  8506 13605  2110  3970 11450  3678  9751  5736
  [983,]  9571 13397  4876  9222  8602 12172  7851 13419 11747  9021  8357
  [984,]   315   766 13280  2544  6929 10078  3303  9530  2801  6962  9297
  [985,]  5386  8497  1328   994  3601    70  1162  1779  1986  4954  2163
  [986,]  6763  8188   786 10523  4048  3872  9024  5320 10325  7387   189
  [987,] 10278  4469 12326  6865 12174 13084  6058  5824 12077 11776  5649
  [988,] 12104 13457 13214  8054  9421 12108 11307  3962 11474 12286 12084
  [989,]  2421  2036  8827 11757  4246 10725  4975 11850  9585  5285 11918
  [990,] 12929  2640 11345  6892  8051  4198  5972  7951  1291 11926  6703
  [991,]  2624 10449  3203 11426  6575  9648 12176  6272  9246  7355  5534
  [992,]  3705  4333  2690  2313  3609   666   566 11218  1758  7537   907
  [993,] 13179  7853  6973 12316 10690 12350  9531  6840  2752 10664 11440
  [994,]  5859 10190  9109   421  2888  3628  1850  4202 11060 10166  9440
  [995,]  6804  2355  8397  1500 11755  5732  6635  3255  4791  2587  8398
  [996,] 11737  4539  9922 11535 10967  7457  7327 12330 12856 12016  7713
  [997,] 10372  5928  6096  9824  3979  6003 10116  5433 10264  4809  3269
  [998,] 12104 12904 10771  6970 10996  8316  9361 12964  8365 12235 10848
  [999,] 13580 10728 13515  9943 13214 10449 11774  6790  6281  2998 10041
 [1000,]  8100  6760  1579  3552  4235 11450  2368 10663  2636  4132  9240
 [1001,] 13641  7654  6691 13037 13148 10509  7275 13289  7216 13349 12658
 [1002,] 11671  2705 13153  3595  7533  7405  2996 13507  7137  3519 11813
 [1003,]  3903  2774  9735  1969  5762  6561  9268  6814 10703  4636  6763
 [1004,]  3275  5877  8195  7878  7724  2385  5562 11017 10256  6007  4438
 [1005,]  5247  6251 12131 11888 10590 13177  7918  5148  4265  9026  5197
 [1006,]  5093 10625  8813  4270  3330  3097  9221  2745  8787 12417  6999
 [1007,] 12812  4072 11522  2488  2947   453  5856 10370  9076  2619  3410
 [1008,]  2638  9980  8844 13075 12845 10941 11159  2080  7202  6123  8868
 [1009,] 10210 11773  6221 10513 13028 10080  4262 12508  6176  8377 12770
 [1010,] 13640 10741 13026 12796  5671  9196  6258 13496  7209 12270 10874
 [1011,]  7290 12806  6161  3522  3261 10896 13397 11733  9247   399   116
 [1012,]  8052  9928  9024 12917  7823  4967 12757  7030  2153  1794  8241
 [1013,] 10081 11531 12894 10896  6020  3005  7422  3927 11701  8919  3734
 [1014,]  6665  6500 13160 13032 12992 10532 10216 11945  9556 13520  7972
 [1015,]  3944   713  4122   955  4004  8569   729   427 10744  2167  2239
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 [1017,]  4931   643 10672  1717 12618  7543  2271  7842 11647  2423  1972
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 [1468,]  6903 12357  4200  6564  8742  5776 10754  8506  9272  9108 12557
 [1469,]  9148 10251  1347 12738  3122  9445  4731  4293 12300 10918 13481
 [1470,] 13098  5574  4766  2663  7634  4560  2360 12689 13314  8333  4941
 [1471,]  5594 12667  9545  1915 10085  5054 11279  2129  5046 13385  9310
 [1472,] 12584  9081  9010 13566  9389 11607  5126  9914 10584  3607  3949
 [1473,]  9060 11719  5377 13006  6325 12973 13507 13252  4382 13323 12583
 [1474,]  6322  9170 12131  2233 10555 11876  2697 13214  2274 10012  6241
 [1475,] 11587 13194 11110  9782 11297  9027 12628  8754  2368 10114 11721
 [1476,]  3264  7260 10108 12333  6195 10239 11576  8341  9105  9019  4119
 [1477,] 12596 12959 13233  3957  9555  9247  4456  4984 13182 11785 13566
 [1478,]  3453  8469  7194  2242 11263 10907  7030 13217  2274 10897  1186
 [1479,]  1628 12900  7989 10009  6658  4474   704 13495 12847 11085 11491
 [1480,] 11292 10696  5083 10889 12262 10055  2434 13186 10647 12075  3731
 [1481,]  4062  4263   650  5585  2307  5298  6608  3763  1210   471  1980
 [1482,] 10326 13075  6755  6863  1375  9428  3051  6814  4794 12416 11888
 [1483,]    72   854   688  1866  1623   398  1014   341  1202  1880  4314
 [1484,] 10726  9829 13684 10903  7009 12860 12741 10787  8538  8521 13077
 [1485,]  6980   735 12094  9610  8598  7614  5583 12068 10239  7225 10204
 [1486,]  2387  3372  1638   764  3152   239   851 12243   497  2694  2418
 [1487,] 10714 10730 13019 12273 11634 12762 13266 12687 12039 12827  7187
 [1488,]  6246 11257 13095  7577  8054  8094  8115  4084  9100  4867  2576
 [1489,] 10371  7162  7215  3033  7910 10238  6743 11653 12379 11818 10223
 [1490,] 13221 11508  8999 12112 11621 11584 11794 11341 12132 12290 12832
 [1491,]  7514  8604  5463 10237  4436  9785  2743  7749  9426  8227  1197
 [1492,]  2857  2201  4223  2849  5245  4092  3244  3929  7520  4211 10169
 [1493,] 12448  7695 10572  1726 12236  8304 13051  7838  2137 12440  4667
 [1494,]  6271  2135  5709  4733  2340  4095  4305  3596  3015 10761  5913
 [1495,]  8024 11643  8964  2763 12206  7806  9365  6919  8374 10652  9289
 [1496,] 10837  5460 10973  2531  6884  4717  1567 11435  3811  6001  6965
 [1497,] 13712 10772 13451  4816 12267 10063 10248 13321  1278 13342 11866
 [1498,] 11276  7700  3713 13549  5620  9121 11794  6844 12109 13064 11854
 [1499,]  6096  6841 11768 10103  8059 12607 12064  6011  2188  2782  5688
 [1500,]   461 10153  7532 11381  5479 13372  7008  9566  8213  6249  8625
 [1501,]   402  3298  2615  6352 10536  8895 11660 11733 13031  4345 12899
 [1502,]  8729   968  5498  3602   376  3566  2261  6979  8387  1179  3659
 [1503,]  4381 11238  3456  6273  7287 12724  4612 13103  8188  5813 12895
 [1504,]  8741  5746  4118  5877  9634  6713 11169  2867 10696  8362 12709
 [1505,]  7604  6443 10534 11748  5607  8426  4913 11810  9506 10559  6939
 [1506,]  7391 10564  4037  9847  4416  4366 10119  7745  9435  8061 11745
 [1507,] 12501  8863 13449  5775 13408 13485 12326  4657  7092  8099 11515
 [1508,]  9159  4341   363  7845  1257  5303 11457  5626    56  4234  2260
 [1509,]  3036  6689  6658 13052  9494  8436 12385 13302  9506 12827  2616
 [1510,]  5198  7075  5979 13459  4913 12233 11350  8499 13394 11502  6993
 [1511,]  4224  9513  6104  5574  7224 12636  5636 10483 12394  1314  3209
 [1512,]  7699  9129  2448  6783  6010  3777  7991 10331  6798  4990  8671
 [1513,]  5935  8941  8944 11484 10311 11169 10481 11822 13119 12787  9005
 [1514,] 11214  1575  4236  6635 11279  7178  5161  1586  8728  7767  9150
 [1515,]  7083  6841  1531 13600 12644  7798  5229 10703  9789  8362 11311
 [1516,] 11956  1779 12128  5051  7501 10903  1487  8401  7944 10411  3166
 [1517,]  9800 13324 13264 10984  2423  4280 10818 10303 12337  6676  7406
 [1518,]  9454 11625  7905  5827 10364 12153  7373 11935  4931 10611 11890
 [1519,]  4730  2976  3239  7623  3111 10691  5349  9453  2802 12241  2820
 [1520,] 10396 13422 13263 10690  6551 13296  7884  4096  9248 13026  2578
 [1521,]  9980  5430 12961 13013 11511 13323  8185 13481 13254 12827  9650
 [1522,] 10578  4889  7523  6210  8037  3258  7718 11721 12162 12529  7243
 [1523,]  2691  2545  7245  1586  5432  1393  2169   315   320  4599   356
 [1524,] 11626  5153  6501 13173  5342 10786  5399  8731 10807 10520  9305
 [1525,]   473  7254  7538  7785  4491  7001  5923  9582 13046  5066  6588
 [1526,]  5325 12794  7197 13287 12360 11404  8928 13340  9242  9095  7467
 [1527,]  8240 10938  1579 13236 12428  8136  1140  9181  2880 11454  3972
 [1528,]  5769 10242 13116  5426 11752  9354  5326 12827  3091  5003  7280
 [1529,]  7922 12276 13368  8256 13565  5617  6735  4123 12906  5582 12363
 [1530,]  4660 10586  1977 12638  7377 12406  5936 13473  8253  8655  1230
 [1531,]  1357 12836  3491  8860  8371 11512 10002  4520  4590  3793  1749
 [1532,] 12394 10221 12820  1502 12894  9280  8827  8215 11056  7892  6236
 [1533,]  5645  7000  7554  9781  7426  3162  4746  7731  1671  8648  6588
 [1534,] 11868  9723   781  3723 11212  9404  4180  4965  5280 10445  9105
 [1535,]  5067  8227  3297  3180  6950 11260  5562  6429  6877  9459  8485
 [1536,]  5536   885  2687  1063  2315   239  8788  1307  2561  5048    75
 [1537,]   465 11370  3499  4228  3473  4346 13404  9735   751  6861  2411
 [1538,]  7539  4156 13148  9786  9090  4929  8775  7635  7788  8970 11485
 [1539,]  5855  5028 11557  8222 12625  5680  8090  2287  7907  8335  5134
 [1540,]  2796  3459  6558  4572  6568  4410  3694  3542  1240  9683   915
 [1541,]  9375  6658 13208  7467  5721  9221 12801  9914 11393 11036  8218
 [1542,]  1422  9611  5025  2368  3446  2585 12697  8772  3392  2368  1203
 [1543,]    35    44   508  1920   142    18  2028    52   738   521   565
 [1544,] 12575 12300 13458  9577 11074 11636  7803 12054 11079  7193  9399
 [1545,]  1165  3234  1807  4466  1073  2295  2113  4326 10373  6970  4352
 [1546,]  2501  4269  3213  2645  6380  9099 13243 12608 13363  1072  8618
 [1547,]  2343  5597  1012 10830 12628  5581 10499  1437  7715  4686  6786
 [1548,]  3957 13292 12905  8677  6955  1574 12440  2142 10964 10218 12126
 [1549,]  2992  5029 11522  8588  1984  5680  7788  5034  7907  7074  7365
 [1550,] 12737 12552 11988  3687 12227 10503  8581  9996  7298 13578 12324
 [1551,]  2018  5166  2618 13246  3263 13150 12170  7576  4401  1625 12167
 [1552,]  2456  2920  9955  4264  8087  5931  8452 11375 12183 11405 10139
 [1553,]  3642 10947 12909 10593  8199 11767  9538  9167 12959  8808  9312
 [1554,]  1995  8572  7247  6171  7494  4413  1327  7818  3421  1301  5551
 [1555,] 12387 13082 13559 11469 13181 12446 11745 12684 13499  8301 12300
 [1556,]  2541  9398 11619 13119  9858 12626 11691 10427  9214 12599 13267
 [1557,] 11381  8008   783  2352  1039 10095  4214  5325 10691  7376  7071
 [1558,]  9612  5996  4683  8515  9676 12215 10534  8301 10008 11500  8918
 [1559,] 10457 10469  4346 11335  5333  8931  3595 12199  5599  1119  5259
 [1560,]  3541  1847   909  3154  8245  2579  2569   520   301   361  2676
 [1561,] 12052  5470  7730  7957  2781 10542 11753 11272  5895 10279  5571
 [1562,] 12364  8093 13289  1112  5354  5244 10618  6568 12636 12529  6207
 [1563,]  7865  4406  2059  7917  6806  7562  7130  5869 12260 12763  8997
 [1564,] 13002  3655 12445 13341 12937  9113 13612   943 13455 12675 12961
 [1565,] 12260 10817  9022  9462 11013  7528 13050  4699  2658  4680 11340
 [1566,]  7572 11191  5344 10642  2466  7926 10889  6542 11964  9624  3442
 [1567,]  7437  1277  3176  6745  6501  1872  2929 13123 13242  8460 10387
 [1568,] 12327  3841  4638 10873 12005  2472 10613  9802  9792  6119 12047
 [1569,] 10890 13294 11966  6820 11661  2808  1717  1098  7523  3999  3516
 [1570,]  2367  4087 11552 10681 12178  6659  4510   166  4260  4793  2572
 [1571,] 12419 12865 12677  6953 13619  9819  8373 13135 12035 12387  9650
 [1572,]  7602 13576  9604  7843  3474  3406  9178  7796 11993  2091  9576
 [1573,]  1451  2877 12912 10897  1117  2404  9407  4887  4114  1453  5993
 [1574,]  7739 10096  9865 11837  3875  7464  6418  3026  7261  7161  9873
 [1575,]  6888  3615 11657  4762  5027  3811  2215  2183 12686  5652 11480
 [1576,]  5411  1889  2394  1696  2566  2590  7075  1271   337  4422 10376
 [1577,] 11430 11709  1600  5004  5865  9248  6681  3941 11079  4756  5511
 [1578,] 11121   719  1278  3109  5159  3117  4305  3342 10721  4022  3783
 [1579,]  2178  3675 11267  4696  3899  7529 12809  2867  9535  1783  6950
 [1580,]  4134  6484  8816  4604  9867 12593  4951 10118  7667  9712 12807
 [1581,] 11738 13446  3797  9068  8500  7440 13418 12940  7097  3495   446
 [1582,] 10493  5873 11738  7694 12407  9685 11599 12562 11894 10090 10298
 [1583,] 11647 11186  7533 11371 12450 11757  9943  8681  8142  8609 11657
 [1584,]  2797  5335  7643  4501  1854   649  3428  2172  3496  2241  5082
 [1585,]  3543  2563  1402  7334  6397  4362  4386  1276 10463   609   240
 [1586,] 13371  1404 10509 12756 12531 12447  8256 13513  8411  3528  8713
 [1587,] 10451  2853  1333 11604  7246  7976  1737 10590 12165  5349 11472
 [1588,]  4995  7109  9379 11664  9625  5758 13347  2434 10761  4745  5674
 [1589,] 10354 12953  6765 11766 10330 10768  7596 10267 12200  9464  6888
 [1590,] 11439 12958 12061  8283  8424  9942  6684  4986 12989 13511  4079
 [1591,]  2992  4830  8178  5348 11195  2852  6673 11561  9178  3613  2555
 [1592,] 11840   600 12314 13473 11697 13214 10183 13509 13253 10676  8758
 [1593,]  5321  5921  3360   307 11243  8914   534  5486  1639  5780  4446
 [1594,] 10980 13171  7149  7584  8790 11757  5574  6429 11834  7258 13516
 [1595,]  2374    77  1266   169  5953  2283  1885  5349  3378  2015   565
 [1596,]  5539  7507  2707  8381  8337  5324   531 13427  9420  8580  1726
 [1597,] 12723 10643 13556  6881  5721  9219 10993 12626 13408 11011 11229
 [1598,]  4514   392 10383 10100  9197  4128   452  9149  7364  9598  3781
 [1599,]  9802  8416 10387  6260 12845  5270 12202 12223  4904  9520  6454
 [1600,]  5129  6762  5066 12822  2866  2389   444  9886  6329   478  6104
 [1601,]  7729 13120 13689  9147 12262 12859 11303  6785  6069  8388  8210
 [1602,]  3434  1785   281  1642  6310  8922  7891  6287  6684  4291  2559
 [1603,]  8128  6208  5359 11685  3369 12939 12598  9604 12299 10937 12174
 [1604,] 11061  9469  2155  2096 12806 11399 12547 13354  3854 13399 12468
 [1605,] 12281 11031 12853  8238  5764  7590  9629 13212 10661  5350 10652
 [1606,] 10018 11463 11955  6949 13623  8267  7523  1081 11470  5831 12313
 [1607,]  5272  6234 11984  9648  3354 11463  7637 11567 10718  1080  7045
 [1608,] 12620  3588  6672  4837 13577  7651  2254 11438  5961  7089 11372
 [1609,]  3551 12481  4088  8314  9147  6381 10004  7810 13060  1070  4455
 [1610,]  9852  5736  4224 12158  3388  5100 11277   572 11721  6578  7121
 [1611,]  7804  4068 11520  2909 12070  5679 12920  5036 13419  7074  6226
 [1612,]  2660 12258  3011  8923  3653  6255  4337  5996  2886  7331  9278
 [1613,]  9311 10287 10855  7147  5616  3582  1436  8247 10136  5703  8547
 [1614,] 10575 10443  6465 13464 12364  5160  8730  6591  8762 12363 10937
 [1615,]  7747  3788 11649  5959 11110  9367  5060 13187  5896  9536  2049
 [1616,] 11100  2306  5708  4688 11347  8971 12547  4119  7436  2987 11473
 [1617,]  5763  5558 12171  7090   400  2245  6137  1551   848  6199  4934
 [1618,] 11198  8546 12261  9774  7415  1826  5426 12223  4990 11269  4893
 [1619,] 12724 12973  4073   911  5825  4500 10512  9222  7560  6908 11882
 [1620,] 12235  9801 11258 10078 12259  9915 13531 11410 12865  2172 11283
 [1621,] 10949 13002 11686 11648  8742  2996  3491 11641  8074 11045 11045
 [1622,]  4380  7965  1890  8198  6534  3352  8544  6024  7688  8470  5942
 [1623,]  5051  4731  2076 11757  8644  8753  6230  5818 10766  2718   954
 [1624,] 11529  7240  4983  5379  2467  4028  5665  8344  5480  2448  5192
 [1625,]  3532   871  2384  2317  6566  3495   222  4538  9472  1958   380
 [1626,] 10462 10872  5681 11831 11945  8858  8747  3759 12156  6079 12808
 [1627,]  4148  7002 10062  6491  2823  5999  7035  9388 12370  6742  4270
 [1628,]  7078  7919  8012  9025 12648  4953 12007  8386  9668 10633  9228
 [1629,]  4558  2622  4460 10655 10730  3485   831   523  3537  9001  4017
 [1630,]  1990   560  1966  8379  4413  4315   180  3531  1722  3809   527
 [1631,]   124   107  3319  1059  4118   149   376  1327   837  3858   860
 [1632,]  9001 12251  7450 10595  4276 10366 11893 10118  8682 10236  7895
 [1633,]  4561  2556  5425  3559  5553   652  3633  5584  2558  7480   907
 [1634,]  5155  2441  9206  5078  2376  7898 11653  5128  4272  2803  2317
 [1635,]  3758  3496  7287  8663  7805  2924  2982 11432 11353  2493  9982
 [1636,]  3611  2553  5415  9839  8271  9042 10679  1530  3426   969  1481
 [1637,] 11967 11399 12745  3805  8857  4128 11003  3824  5201 11980  2655
 [1638,]  4872 13147 12853 13281  6763  3701  3440  5052 13566  5697 12131
 [1639,] 13136 12098  9922 11559  6656  7516  5056  5793  3590  8345 12964
 [1640,]  7437 10585  6136 12251  6518  7302 13406  9740 13615 10413  9560
 [1641,]  5586  8546 11765 10607  3575  7785  9054 12565  3307 13382 11187
 [1642,]  8892  4989 11552  2151  9527  4995  4511 10309 12746  1231  5166
 [1643,]  2313  4472  6613  2397  7663  1417  4981  5655  7409  9399  4603
 [1644,]  2593 10619  5591   593  6121  6060  5991  2010  6083  7595  4560
 [1645,] 12552 10304 11520  6134 13201 12127 11504  8268  7955 12700  6316
 [1646,] 11361  2704 11847 13547 12499 12433  2188 12689 10556  7703  8722
 [1647,] 10466  7338 10946 13544 10656 13556 13399 10481 11780  8449  7426
 [1648,]  5810  8203 11034  3405  5055  3024  8682  5264  3094 11068  6194
 [1649,]  8138  1520  6153  5336 12832  7084  5362  8168 10006  6082  7952
 [1650,] 11004  3259  9202 12370  3353  7823 13173 11600  6368  9236  2782
 [1651,] 11647  7292  3474  9787  7466  4008  4346  9709  8736 10518  6038
 [1652,]  4173  3352  4643  2620  3417  1906 10663   988  5784  2234  2737
 [1653,] 12241  4020  6194 11660 11123  2951  2478  6352  8652  4987  1448
 [1654,]  4825  5029  7046  8574   619  6643  8837  6144 12978  1825  5251
 [1655,] 10799 11099  1236  6125  5004  4818  2816 11644  6814  8523  3416
 [1656,]  9570 11046  5697  1501  3957 12131 12855  7215  7254 11462 10559
 [1657,]  1619  8037   499  3964  4992  4851    52  3205  3349  9556  6547
 [1658,] 11716 12536  8695 13069  7814 13411   703  4831 13505  9390 11242
 [1659,] 10876  8040 12831 13088 12952  4506  4448 11538 11072  9447  7339
 [1660,]  5270  3925 11984  7971  8132  8123 12045 10943  7337 13075 13228
 [1661,] 11303 10165 12830 12175 11621 12102  9843 13027 12969 11576 10436
 [1662,] 10578 11981  6361  4840 11233 12317  8772 12555  3061 11956  1472
 [1663,] 10899 10205  1524 12329 11027  5624 12880 13210  5121   141  3624
 [1664,]  9707  1491  5627  7043  9167 10858 13551 10092 10900  2775  8055
 [1665,]  4235  5272  7238 11015 13355  4315  7949 13428 11971  9166  6510
 [1666,]  4173  3351  3685  2017  8231  9777 10663  2010  5781  2233  3555
 [1667,] 11401  2672 12701  3774  6830  9355 12307 12396 12540 10565  9692
 [1668,]  2682 10538  2255  2794  6549  3479 11479  2166  2549  4856  4008
 [1669,]  3820  8331  6268  3460  2285  8609  4766  4325  2400  2839 12251
 [1670,] 12293  8327 10284  4986  5872 12572 12986 11021 10397 12908 12171
 [1671,] 12459 12700 13328 10920  4860  2069   751  6113  8933  8318 11536
 [1672,]  2985  5078  2510  6807  1446  1634  2874   794  5713  2008   607
 [1673,]  6214  6967  8063  1580 11233 12303  7667 10984  8604  5229  8849
 [1674,] 12336  5726  9796  5870  9828  9719  8539   580  7672 11446  8090
 [1675,] 13190  4507  9790  2515 12812  7976  9288  3878  3887 10741  5937
 [1676,]  4558  1850  4438  4110   830  1952  6915  5535  3530  7031   576
 [1677,]  3590  3692 11163  7105  6549  6106  9538  4926  2646 10499  1541
 [1678,]  5076  2058  5614  7507  8297  7800  7197 11352  6415  7241  6914
 [1679,] 10853  5453  2798 11469 10366  6531 10183 12700  7649  8865 10546
 [1680,] 11536 12405  4638 11873 10543 10869  5369  7305 10816  9728  9826
 [1681,] 13249  8820 12788 11516 12592  9262  1167  3962 11477 12287 12477
 [1682,]  2886 13546  5446  6753  8360 10434  7081  4503  4628  9595 10383
 [1683,]  6654  7028 11486  1497 13175  4500 12139 11538 12713  9360  4072
 [1684,] 11852 12082 12719 11747  9284 11015 11185  6901  5966 11299 12384
 [1685,] 12087  3009 10652 10910  9319  7475  8569  2233 10628  1199 12325
 [1686,]  8026 11808  2110 10345  2032  7792  4293 10261  6365  7828  6895
 [1687,]  4833  8034 10039  7538  4880  5681  8090  7489  6737 11177  3189
 [1688,] 10908 12623 12733  7626  7873  6697 13659  9129  7222 10302 10700
 [1689,]  6248  7375 12562  2242  9796 10355  6797  6212 11782 10030  5197
 [1690,] 10005 12083  5534 10339 10848 13493  8361 13383 13397 13446  7905
 [1691,]  4227  6953 10891  6070 11159 12599  4486  8381 11831 12140  8407
 [1692,] 10254  3025   806  6122  2078  4862  2624 11071  9370   777  7500
 [1693,]  3116  9216 11626 10033  6908 10647  4251  2281  7698 12070 11958
 [1694,]  5884  1696  4655  3849  7834  9293  6447  1628  9704  5858  8821
 [1695,]  5991 11126 11034  1826  5986  5770  5580  3278  6816  2690  5269
 [1696,]  9893  8441  9579 11332  3393  5161  7717 12550  7366  6407 10006
 [1697,]  2712  5328 12296 11411  3634   907 10008 10559 12011  8498 11744
 [1698,]  8922  6996 10914 12753 10804  8060  1956   290 13194 12346  7692
 [1699,]   384  8643  1585  1862  4608  3472  1828  1035  3520  4836  5082
 [1700,]  7701  8705 13298 10734 12858 13203 10141  6883  8388  9820  7964
 [1701,]    92  2584   360   883   314    53   218   543   318  2544  2594
 [1702,]  1159  5409 12189  3394  7036  3018  2278  3908  7808  7822   244
 [1703,]  5334 12458  9559  9834  9077 13308 10112 10484 13211  4301 11799
 [1704,]  7288  6269 11139 13366 12458 11876 13651  3339  8193 11196  6346
 [1705,]  7836  5972  1767  5424  1563  2245  8626 10395 12144  7375  2055
 [1706,]  9684 12456 12147 13397 10068  7173  7918  9368 11783  6094  7353
 [1707,]  5910 12652  8377  4378  6941  8551 13442 11461  3584 13537  9307
 [1708,]  3201  7269  8221  7266  1295 11264 10799  4058  6673  6067  5169
 [1709,]  4670  1423 13688  2801 11101 13089  9559  2865 10685 10345 11845
 [1710,]   414  2627  4648  7831   511  6331  5446   988  2585  7877  9091
 [1711,]  8759  9297  8915  5827  8565 12545  4283  6125  8650 13268  9003
 [1712,] 11067 13595  3128 13246 11858 10301 10773  1811 12776  6775 10989
 [1713,]  2018   624  1163   593  4145  3233  2219  2743  1427  3162  2653
 [1714,] 13091  5951  2951 10143  8514  7500 10464 11531 12118  9914  6938
 [1715,]  9126  1561 10414 12560  7988 11396  4366  7097 13296  8591  3050
 [1716,]  4601  8092  7490  7200  1527  6017   618  6378  5684  3463  3345
 [1717,]  4468  2125  1161   393  4138  8822   743  1951  1483   980  6101
 [1718,]  7311 12463  1502  3342  9194  8152   281  4122  9839 13022  9074
 [1719,]  3905  1175  3927  6080  6747  4625 11536 12465 10191  3591  6316
 [1720,]  9045 10403  4082 12228  7408 10343  8967 12862  8054 12336 11055
 [1721,] 10166  2356  7307  2221  2083  3778  5707  9492  1601 11852  7500
 [1722,]  2278  8333  7418 11300  1597 12204  6865  6360 11891  7983 13557
 [1723,] 12792  8850 13451  2780 11711  8314 11118  9999  8471 11748 12509
 [1724,]  2538  6892  3127  6204  3595   531  7043  5375  4274  1925  2580
 [1725,]  9657 10867  9042  9949  7198  1710  9764  2011  9913 11385  6123
 [1726,] 12195 11526 12032 11778 11084  3606  7428  5920  6036  8791 10842
 [1727,]   351  7806  8808  2770  1368  6871 12432  2020  2097  6909 12781
 [1728,]  6856  9378  9393  7895  2222 11740  9070  5264 11247  6964  1284
 [1729,]   944   955  2837  1374  2352  3241  2946 11922  2102  1432  1898
 [1730,]   327  1489  8011  8039  3776   704  2391 10672   900  7118  8265
 [1731,] 13293 12709  5695  3851  9611 13422 12856  5230  9684  8313 13206
 [1732,] 10938 10317 10854  2996  2926  7621  5854  1114 12360 10189  7551
 [1733,]  5613   353   930  2068  1244    85   506   157   193   977  5079
 [1734,]  4919  4936 12609 10534  8758  2992  4473  7521  5554  4788  2341
 [1735,]  1809  7556  1449  9504  1169 12588  8199  3692  2993  5183  6923
 [1736,] 13158 11740  3719 13651  6907 11192 11988  2281 12139  7135 10662
 [1737,] 11939 10935  8808  4672  4792  7816 13304  9955 10898 13401  9038
 [1738,]  7882  6858 10732  8081 13661  5654  9450  4620  8623  3605 10927
 [1739,]  3880  8839 13444  8458  2790  4557 12379  9810 10844 10161  7181
 [1740,] 11716  8811 12007 12058  9377  1023   751  5001  8543  9320 12685
 [1741,]  7095 11206 10101  9661 12852  5965 12892  9383  2076  3671 10144
 [1742,]  1109  2612  2690   851  2705   648   641  7796  4628  3910   377
 [1743,]  7410 10545  5033  4051  9129  4379  1984  8770 11972  5625  4297
 [1744,]  3526  3464   764  4229  3634  1980  3559  4572  3404  2819   915
 [1745,] 11555 11929  3123  8337  5177  9641  8919  1676  8923  6787  3009
 [1746,]  8478 10085 12838  6033  2901  8272 13665  8197  5361 12566  9403
 [1747,]  7625  1913  9626 13469  5603  5401 10129  2002 13266  8671  7717
 [1748,]  4416  3451  5879   608  6407   663  1848  2965  1831  1768  5083
 [1749,]  1073  6378  3497 10650  2305 11503 13515 12887 10455 10118  9619
 [1750,]  8869  6182  5659  5403  3352 12892  9647 10222  8941 13310 13054
 [1751,]  4349 13197  7284  9416  5308  8922  9910 13052 11046  9026 10230
 [1752,]  8667   611  3189  7914  2032  1412 11986  5826  7691  6566 10576
 [1753,]  4697  3502  6167  3717  4825 11699  6013 12383 11326  6484  7731
 [1754,] 12052  4473 12299  7961 12535 13209 12717  8908  9496  8291 12750
 [1755,]  4874 12735 12095  6456 11032  2088 10760  7231 11019  5696 10436
 [1756,]  2543  9375  8195  6066 13587 11817  8891  9390  7953  9108 13381
 [1757,] 13276  8268  3038 11208  9597  5500 12983 12057 10124 12136  8557
 [1758,]  5536   336 10479 11988  9977   148  2081   525  1257  1610   869
 [1759,] 10636  1788 12640 13503  1780  6262  4646  2505  1695  9031 11798
 [1760,] 11118 12814  1945 13456  5479  2548 10944 12869  8207  8500  2400
 [1761,]  9159  6398  6551 12633  5507 11983  5455  4495 11978  2081  3795
 [1762,] 13087 13373 13343 10798 13213  9901 13041 13298  8331  8835 10551
 [1763,]  6721 11528  9018  4549  6668  8388  3172 12680  8476  9396  1532
 [1764,]  9574  8233  8446  7656 11816  4779  3510 11087  5549  5022  7494
 [1765,] 12874 11138  8104  6338 10194  7495  9834  3989 12331  1823  8378
 [1766,]  2508  6808  6413  9759 10578  9524 10589 12767  4882  7011  8941
 [1767,]  8749  1373 10562  8985  9456 11167 11729  9818 10524  9207  8015
 [1768,]  7967 12857 11333  8976 10330  7741  9210 12300  8367 13289 13041
 [1769,]  7070 11422  9772 13388  6250  8656  7190  6962  5148  7322  9064
 [1770,]  3449  7345  8286  2436  4269 12721  8141  5461  4298  2527 10362
 [1771,]  6653  5367 13294 12261  7507  9835  9188  5711 12857  9691 10589
 [1772,] 13496  5678  1898  6772  8856  8958  3190  2192  3066 13522  6045
 [1773,]  7150 10870  8052 10779 13336 11781 11227  9172  6486 10665 13048
 [1774,]   672   872  1400  2320  1314  6373  1981  5612  5838  1304  4456
 [1775,]  9565  5715  1543  7616 11179  3727 11367  2154  1490  2158  6914
 [1776,]  2101  9585  2618  5200  2405 12929  2763  4363  1683  4423  3349
 [1777,] 10121  7607 13298 12781  3863 11039 11722 12697  8388 13107 13539
 [1778,]  5288 12789 11169 11324 10825  8066  8921  2532  1666  4964  4447
 [1779,] 13488  5692  9010  9030  3733  7566  5319   564  2935  5717  3946
 [1780,]  8500  7586 11848 10310 10848  9881  6041  6817  7151  9307   926
 [1781,]  5990 12730 12908  7219  4961  8568  2454  8456 10100  6416  4839
 [1782,]  3166  1268  7904  3706  7056   926  3417   618  5788    78  1998
 [1783,] 10972 12029 11322  5738 13230  3098 10166  3722  8847  9706 11429
 [1784,]  3459 10129 11116  8727 10547 11882  7921 13096  8152  6085 12538
 [1785,]  2013  2528  2339  2341  3428  8220 12106 11206  4554  9503  1366
 [1786,]  4730  1087  3240   316  1015  4831  1770  2216  2798  7685   469
 [1787,]  9053  8984  7919 10066 10585  1793 10487  7087 12162 10782  8853
 [1788,]  5763  4450  8940  6854 11502  9287  3051 11356  5996 12698 12346
 [1789,]  1671  6125 10290   844  2298  3938  3763  4330   470   864   851
 [1790,]  7024  8205  7869  6146 11053 10711  9643 11564 12902 13268 12979
 [1791,]  7484 11242  6363  8720  4384  1237  6954  8645  6548 10072  9595
 [1792,]  6937 11561  2193 13228  5902  7563 11160 10061 10600  5949  3492
 [1793,]  9912  2990  5229 13179 12780  1802  6256  2129 10776  7760  2239
 [1794,] 11317  6061 12518 10920  8708  9954  7780  5218 12320  4264  6422
 [1795,]   785 12622  5111  3175  4046   193 13049  3911   876  7443  3746
 [1796,] 12638  4841  8434  4448  5069  5841  3656  8486  3317  6717  5423
 [1797,] 11601  8094 12877  1192 11295 12964   534  6242 13192 12959  7512
 [1798,]  8080 10324  6104  3571 11784  2394 12260  2423 13211  3230  3456
 [1799,]   197  3196  2291  6479  5808  5668  1903  1134  9170 13159  7362
 [1800,] 12147 10739  9903 13041 12601 13402 12751 12966 13404 11748  9745
 [1801,]  1451 11206  3426 10677 12450  7939 12892  1831 11725  6302  7118
 [1802,] 12193  2242 13217  8085  7624  1023  1726  2231 10647  8113  2752
 [1803,] 11530  9988  6942 11154 12823  7826 12892  7349  7727  1951 10906
 [1804,] 13696  2159 10646  6926  7288  6189 11969  2063 11657  3993  7057
 [1805,]  7784   404  7335  9675  3117  4822  5196   435  1338  8937  2828
 [1806,]  1674  2825 13432  4680  5772  5597  8340  5671 12882 10634  3891
 [1807,]  8867 11883  7167  3342  9238 10790 12540  6266 10794  7265  2781
 [1808,]  2501  6014  9191 12964  6790  6004 10758  1700 12751 10388  8372
 [1809,]  5474  2564  2418    75  3449  5330  4407   584  5750   209  2679
 [1810,]  5341  5480  8840  7973  4275 10360  7197  3756 11565  1486  7760
 [1811,] 11742  7735 13193  4654 12588  3530 12324  7867 13078 11387 12066
 [1812,]  5844 11839  7040  9237 11526  2899 13225  5073  5401  4713 11112
 [1813,]  2792  3385  1963  1219  5444  6376  5712 10563  1722 10555  2594
 [1814,]  6870  4582  9682 11762  5611 10633 11158 10672 10540 12303  7882
 [1815,] 12422  9756 11264 12517 11518 10548 12373 12321 10556 11099 11231
 [1816,]  7629  9729  9646  8983 11637 10551  8274  7955  8382  9400  9717
 [1817,]  5319  8088 12880 11281 11358 13306 11591 13050 11880  9089 12148
 [1818,] 12256  4827  5939  7177  1993  6617  3440 12782 10604  9404  6233
 [1819,]  1184  7197  9400 11915  7050  2287  9018 13238 11174  9569 11173
 [1820,]  2886  7526  4407  9380  7439  4349  5945  9735  5743 10541  2411
 [1821,]  6115 11191 12111  5244  5531 12293  1318 10308  4300  1931  9504
 [1822,] 11031  3699  6970  2414  8932  8089 11948  3630  6084 12822  9240
 [1823,]  5854 11094  1242 10520  5058   513  6872  9541 11889  8536  5450
 [1824,]  2437  5177  8206  4216  5229  5901 11644  7258  9121  6695  3266
 [1825,] 12671 10870  8818 12686 13115 11457 13318  1465 10910 11334 13365
 [1826,]  6569  3065  6346  2999  5005  4926  1381  8510  1631  5582  3231
 [1827,]  5134  5986 11390 12858  2839  6891 11345  7343 12577  7609  9762
 [1828,] 10680 12042  6676  7913 13190 13021  3918  8961 11646  9350 13417
 [1829,]  2526 12949 10612  5525 12416  9507 10422 13418  7668  8757 10746
 [1830,]  8075  2952  4353 10104 10795  8720  6318  6024  8584  7255  5045
 [1831,]  1292 11206  9960  7882  3236  4081  7698  8371  1490  6644 10912
 [1832,]  4697  6510  4529 13015 12981  8273  1563  5635   561 10329  7735
 [1833,]  1531  8903  4283  8911  6086  1721  3187  3925  1506  5096  1541
 [1834,] 11422 12207  4715 13576  7752 11610  8585 11347  8824 12074  4518
 [1835,] 10293  7812 11424 12930  2849  6596 10410  2780  4833  9393 11982
 [1836,]  3272 10364  8248  6178  4192  3191 10067  8379  3186  6748  8690
 [1837,]  7197  9472 12124  8303  8900 11405  4535  6207 10167  5481  6243
 [1838,]  7612 11773  4715  6048  7753  8396  7560  7167  3029  1808  9918
 [1839,]  5225  6558  6153  6771  9241   361   396  5738  2920  6075  8945
 [1840,]  9853  8528  6387 10097 11846 12912  7705  8625  6577  7621  4855
 [1841,] 10468  8943  3342  7417  7175  6215  3129  9797 12866  7018  6846
 [1842,]  5129 10931  3784  8016 13428  7826  5332  8987  2931  6368  4740
 [1843,]   380  1278   770  4529  1228 10430  5953  6709  4613  2393  7609
 [1844,] 12678 12952 13129  4859  9841  3325  8747  8148 11591 11406  8331
 [1845,]  9556   926  6612  4628 13487  6623 10180 12405  4949 11424 10566
 [1846,]  2726  4257  1724  5638  6394  3452  2571  7775  5765  1761  5808
 [1847,]  7432  3451  5023  1623   806  3405  2933  1328  1256   646  5414
 [1848,]  1532  3435  6540  4779  1914   960  9816   266 12005  1380   475
 [1849,]  6614   100  5418  2626  9977  1906   158  6054  4598  7029   702
 [1850,]  6959 12275  8144  9631  2828  3685  7846  7259 12367 12181 10197
 [1851,]  9018  2662  2163  9568 11346  8998  1611 10089  1404  5402  9974
 [1852,]  9324 13006 10044  3896  4654  3526 12982  1093  5388  4633  3238
 [1853,]  6874 11034  8114  9591  4872  7504  5521  7178  6454  4760  6382
 [1854,]  8799 10322  7411  7762 13610  5839  3765 12126 11923 10942  9491
 [1855,] 12888  9044  4072 10678  3816 13342  5126  5855  2116 11034 10139
 [1856,]  3069  1059   788  1148  4052  2205 11814   208   405   940  1011
 [1857,]  4654  6956  5299 12877  5551  7014  9039   819  2895 11896 11209
 [1858,] 11733  8850 13567 10011  8486  9173  8319 12951 10501  5885 12491
 [1859,] 13209  8023 11359  2915 12881 12818 11283  9241 11474 13220 10522
 [1860,]  1449  4296   473  5137  3442  2683  5695  1860  5820  3316  5522
 [1861,]  5667  8661  5577  4613  9366  5521  7127  9828 11620  2106 12333
 [1862,]   672  7371  7286  3554   755 11425  8112  8430 10303  1625 10437
 [1863,]  6081  1203  7117  6146  8926  8650  7894 10950  7913  6695  4115
 [1864,]  3352  9482  9251  3045  5205  9697  9589  9374 12159  5231  7211
 [1865,] 10201 11565  8996  8490  4742  3667 11225  5821  1450   944  1521
 [1866,]  6633  7865  6406  9194  7466  7833  2536  7131  6095  7496  6040
 [1867,]  8898  3675  4551  3819  3901 11780  1131 12413  5177  7563 12784
 [1868,]  9164  3458  2015  5264  5444   408  3647  5627  3546  1606   858
 [1869,]  7553  6713  6501  9198  3387  8987 11276 12022  3668 12505  9155
 [1870,]  8443  6424  5459  7848  2610 10987 12113  6673  4556  3151  2918
 [1871,]  1335  2467  6828  7510 11452  8740 12064  8381  1490 12724 11942
 [1872,]  7285  9460  1658  7619  6307  9686 13372 10259  6689  8450  9470
 [1873,]  7625  6442 11840 12461 12220  9929  9231 12971 12037  8828 11240
 [1874,]  4622 11978 13286  7725 10589  5281 10029 12569  8121  9032 13558
 [1875,]  6164  4104  3959  8652  2027 11373 10076  9367 11108  4790  9531
 [1876,]  7873  2825  6231  7055  2961  6703 13266  5635  8428  9565  1005
 [1877,]  2049  9469 12934  9338  4220 10301 10772 10440  6868  1634 13120
 [1878,] 12987 12850 13493 11470 12664  9219  9281 13316  3635  5880 10482
 [1879,] 12162  8172 12428 12571  7815 13357 12022  9240 12144 11130  9754
 [1880,]  2742 11952 11177 12996  4359  7978  8753 11720  8986 11397  7130
 [1881,]  8265  9669  3994 10246  6389  4322  4561  8794  2456  9160  7572
 [1882,]  8819  5406  9850 10732  3031  3998  4283  8873  5001  8763 11890
 [1883,] 11990 11248  1866  7876  7193 13178 13376  1806 11195  9048  9645
 [1884,]  6110  3351  2845  2794    19  4372 11468  1468  5781  6654  2680
 [1885,]  9554   926  1432  8504  2849 11696  2200  5887  8665  6409 12020
 [1886,]  9673  4870  4631  3189 12763  7949  9687  4109  6076  5177  7923
 [1887,] 11266   986  1203  8180  3097  1601  3953  2993 12072  4977  9108
 [1888,] 12524 13371  9920 12120  6660  9179  5114 12678 11377 11773  5588
 [1889,] 12042   347  5466  8896   558  7302 10689  5624  7018 10554  2126
 [1890,]  6160  3265 10114  5096  3347  6044 13206 10996  3186  4376  4439
 [1891,] 11445  9899 11362 13664  9307  9309  3098  6821 12583  8914 12353
 [1892,] 12286 11564  9740 11782 10373  2875 13086  2939  6406 12850  9838
 [1893,]  3941 10105  7056 12862 12173  3686  7815 12072 12993  7193 10965
 [1894,]  8083  6177  7215  1654 11913 13134 13207 11160 11836 13326 13271
 [1895,]  1747 10329  1627  1673   932  3733   974   725 10231  1005  1141
 [1896,] 12964  7250  2628  6801  1207  1202  9088 12580  2380   890  2582
 [1897,] 11116 10465  9962 11173  9182  8008 11383 12178 10726  2811 10130
 [1898,]  9926 13234  6489  8200  6522  9462  7640  6028  7489 10517  4893
 [1899,]  9556  4591  9694 11133 11808  5642 12447  8098  8377  3444  9913
 [1900,] 10659 12468  7523 12989  6163 13447  8070  6590   713  6783 11169
 [1901,]  4393 11601  6967 12835  1918  4243  4152 12750 11383  7285  8259
 [1902,] 10610  2281 12935 10990  8070  3355  1705  6579 12161  2127  2899
 [1903,]  9040 10399 10090 10470  4239 10943  9752  4052  7746 10581  9855
 [1904,]  9584 13178 10883  2926 12738 10658  3444 12498 12719  3570 10987
 [1905,]  3919 11556 10678  6983  5783  4611 12007  7842 12578  4649 11907
 [1906,]  4126  1395  2073  3611 11903   516  8199  3703  2993  7549 11996
 [1907,]  5595 11140  7485 13265  7913  6953   983  5427 11922  7907 12573
 [1908,]  4310 13596 10349 12883 13077 10310 12603 11179 10349 11606 12536
 [1909,] 12403  1186  3920  5350  3873  2064  7772  7203  5386  6721  8518
 [1910,] 13594  6571  8720 13214 13530 11091 10369  9877  5912  7703  7967
 [1911,]  8712  9196  9398 10282  2281  2273  3724 11633 12449 11856  5423
 [1912,] 13157  3662  3712 12485 10373  5561  7337  8854 12094 10278 12353
 [1913,]  5028  8276 12856  3352 10286  3755 12656  3079 12325  2574  2373
 [1914,] 13418 13376 13214 13346 12937 12074 13539 13456  5928 12682 11528
 [1915,] 11225   619  1436  4613  4644  2045 10155  4655  1931  5188   124
 [1916,]  5671  1397   735   119  2853  8285  1035  8845  8773  2421  5568
 [1917,]  9032  3089 13263  9310 11356  7214 13211 12106  6755 11573  3213
 [1918,]  4194 10257  8227  7611  4778  8810  4530 11602 11835 10952  7465
 [1919,] 12256 10821 12010  9485 12142 13084 11134 13167 13133  7820  8899
 [1920,] 10918 11066  7958  6048  5966  8452  7560  8293  4078  2407  9917
 [1921,]  7756  9354   502  3978  2069  1117  4765 11661  5680  3625  3243
 [1922,]  8876 12245  9949  6387  2026 10772 12410  6952  9667 12877  8298
 [1923,]   473  7212   816  2432   391  1691 10930  1759   274  2066  3246
 [1924,]  3111  1449  7278  1717 11197  5646 11772  9785  6423 11164  7940
 [1925,] 11953  6747  8899  1984  5205  1787  1159  2010  9913  4009  4569
 [1926,] 11847  1533 12765  8081  2900  7350  3100  4827   595  7690  2205
 [1927,]  4516  9082  7559  4405 11966  7832  9538  4923 12650  8610  3801
 [1928,] 13191  7900 11078  8703  8154 12308 13133  2924  9022  2204  4871
 [1929,]  7460  8110 12660  6236  3659  8939 10107  6628  6954 13042 12641
 [1930,]  6516 11934 12243  8749 13325  7138 13594 13087 10349 12601 13512
 [1931,] 11290  9796  4508 10358 10351  4468  9362   655  2626  4439  5743
 [1932,]  3759  9334  8091  5338  3695  1449  2085  3042  3115 11542  1167
 [1933,] 12474  8752  5571  8496 13196  9918  4047 12318 13415 10316  7881
 [1934,]  8874  9310 13370 12370  7717 11319 10546 10277  9944   448 12016
 [1935,] 11847  5453  9695 13021 12659 13322  7203 11950  4938 12488  9700
 [1936,] 11204  5328  8673 10255  4458  1401  3665  8840 12488  2373  3426
 [1937,] 10899 11055  8889  6020 11671  5620  8651  7212  7304  5691  8843
 [1938,]  1505  1339   934  2340   558   636  4713  1897  1838  2927  1812
 [1939,]  8113  2876  6975  7402 13345  7981 11961  6784  5126  9234  5012
 [1940,] 10405 11225  6872  9562  6214  5248 12909  8398  6368 12554  4675
 [1941,]  8763  7814  6600 13484 13417 12518 13445 12962 11485 12870  9901
 [1942,] 10380  3711  9967 12534  9794  1771 10323  7953  2646  9868  2632
 [1943,]  7674 12603  8015  9181  5841  6685 12342  3796  1276  6891  9717
 [1944,] 11058  5891  5708 10873 11981 11387  6541  9377  8586  6068  9962
 [1945,]  9297  9796  4615 12057 13534 12793  3102 11299 12572 10759  7789
 [1946,]  4361  1233  3103  4075  8156  6175  8151  5416  2297  1743  4260
 [1947,] 10802  8874  1203  2086  4002  2245  3185  2994 10596  6199 10077
 [1948,] 13658  2121  2408 10820  7745 10558  9393 12328 13416 11113 11533
 [1949,]   727  8349  6506  8360  4472  5046 10107  8595  8177  5066 11681
 [1950,] 12697  3952  5344  3146 10080  5958  2524  7635  1992  7492  6207
 [1951,]  7046  3613 10682  9536 11452 11263   407  3779  6370  4811 11942
 [1952,]  2916  5824  1814  6122  5864  1084  3468 13342  1604  7368 10282
 [1953,] 12052  7616  9644 12271 13179  8350 11760  6875  9532  9404  9815
 [1954,]  5459   911   287   465  3554  6360  1373  4563   784  1978  3325
 [1955,] 11911  1944  7788 12467  6749  5577 13025 13537  3632 11921  5569
 [1956,] 13438  6761  5822  5780  8647  5432  3276  2002  9893 12973  4928
 [1957,]  8796 12749 13370 11879 13318  3742  7846 10223 13423 12121 10215
 [1958,]  9759   617 11947 11823 11221  5142 10182 12022  6431  2115  7872
 [1959,] 12735 11011 12053 10907 13640 11125  7541 10151  4803  6443 12068
 [1960,]  3499 12484  3170  4110  1314  1949  8807  7822  3530  1958  2246
 [1961,]  1770  7522  1828  5588  5092  3406  4887  8836  4612  2859  7603
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 [1963,]  1136 10999   809 11376  7944  5830 10897 10337  9392  2838  5423
 [1964,]  8081  1742  4006  7311  3640   534  4842   302  5492  1925  1879
 [1965,]  3910  5608  2462  6555 12304  4763 12433  2937  7780  7431  3754
 [1966,]   913  9025  7943 13138  7909  8757 13112 13009 11583 12799 12788
 [1967,] 11763  7051  8127  7138 11636  3634  8841  6106   660  1680  2270
 [1968,] 12705 11839 10035 11616  4845  4517  9095  9244  7895  2597  1168
 [1969,] 11449 13287 10523 13654 11642 12141 10236  5797 13504 12481  8713
 [1970,]  6018 11171   466  4978   935  6658  3765 10223 12742  3251  7371
 [1971,]  6774 11159  4155  3937  9579  8586  3459  7442  6905 13317  8398
 [1972,]  9325  6579  7730  9038  2781  9237  8374 11825 10541 10249  5566
 [1973,]  1301  4733  1559  4321  3010  4977  6237  7107  2065  3671  9269
 [1974,] 12128  9323 13229  2485 11520 11621  9821 12054  7878 11541  3115
 [1975,] 10068 12091  4528  7497 13271  5694  8433 11434  8462 11084   928
 [1976,]  7125   798  1731  5051  5207  9548   620  9356 11781  9023  7385
 [1977,] 12905  6510 11859 12446 10912 12143  4979 11361 12018 12297  3485
 [1978,] 10369  7889  6718 12666 10643 11296 11246 12441  9982  4897 10763
 [1979,]  7650  3026  2447  7623 11752  9356  6638  7491  3212  7397 11051
 [1980,]  6297  2791  6822  4274 11995  8843  7665  2930  6099  1945  2705
 [1981,] 12963 12816 11153 13112  8924 11418 12605  7692  9315  9105 12874
 [1982,]  9216  7507 11819 12905  8339  7275  4658  7778  2481  8653  4374
 [1983,] 12625 11095  3263  8911  2251  8578  6491 12507 12175  9553  6187
 [1984,] 12026  2303  7553  3145  3574  7897 12214  8730 12440  8643  7624
 [1985,]  9159 13537  2707  6302  8338  9050 11446   210 10438  7462  4859
 [1986,]  7411  9616  2253   515  9954  4353 10694  6723  1749  5444  3090
 [1987,] 10826  2230  7368 10944  7787  1539  4447  4175  3222 12143 12869
 [1988,]  8388  6806  6409  8187  7023 12881  6314 11461  7486 13492 10936
 [1989,]  7119 11599  8049  8541 11902 10738  9721  4782  3736 11523 11571
 [1990,] 10630  9502  9531  6234 11435  9009 11546  4465  6895 10525  8543
 [1991,] 11792 12597 12797 10792 13562  8355 13261 12951 12663  8835 12834
 [1992,]  5894  7100  4188  7644  4059  7690  2783 10402  5562  5548 12921
 [1993,] 13394  9813 11378 10309 13398  8355 12372 11299 12665  6598  6902
 [1994,] 13653  9757  8772 12471  7566  9818 13107  2731  3561 11919  8990
 [1995,]  5512  9998 10456  4877 11410  7090  2403  3843   848 13526  3807
 [1996,]  7953 11861 10299  5035  7017 12576 10101  6318 11235  7426 13406
 [1997,]  9899  9455 10384  9322  9197  4159  1706  8727 10978 10521  2890
 [1998,] 12256 11646 11362 13656  9307 11196 13530 11904  8631  8924  8956
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         [,34] [,35] [,36] [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44]
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    [8,]  5684  5568  5617  5339  3140  7480  5549  9480  4519  5353  5998
    [9,]  6151  4838  3271  5214  2011 13593 11311 13382 10620 11048  1575
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  [146,] 13328 12485  6115 12805  7780  4191  7008 12166  2299  8368  8681
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  [230,] 13004  4445  3661  3072  9157 11511  2395 11412 12451 11684  8117
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  [330,]  3086  4019  6311  9482  3851  7259 12671  4167   714  7005 12895
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  [360,] 10964  3894  3362  1857  4274 10022  7795  3585  9783  2423  2809
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  [368,]  2137 10692  8264  6105  4613  8637  7490 11200  9459 12187  3575
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  [464,]  3165  7160  2655  3838  7200  9949   627  1867  1052  6790  5825
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  [477,]  1992  3572 11765  6500  2176  2481  4524  4016  2497 11797  7540
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  [482,]  1315   519   599  8493   643   398  4427   105 12518  1918   100
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  [521,]  6072  3899  6837  4156  4904 11834  4236 10520  6599  8476  6457
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  [523,] 12544  3691  6890 12228  8449  8741  5216 10358  5090  2167 13582
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  [525,] 13422  1248 10217 13334   917 11346  7014  6222  6114 12339 10531
  [526,]  4156 13275  4124   273  4038  3556  6633  9982  9660  1586  6679
  [527,]  9246  1052  1920  7416  4376  4830  3784  4262 11150  2860  6891
  [528,] 11638  9885  6795  5967 11520  6808  7491  8873  3249  9216 12147
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  [531,]   704 12578  7663  9690 12835 13051 12873 13162  9018  7727  6303
  [532,] 11079  3930  7304   807   547  5077  5243  4235  5184  5790  7935
  [533,]   262   692  9394   374  1000  1740  6290   396  4664  1313  3232
  [534,]  1650   889  6898 10219  7295  7696  9269  9824  6209  9118  6319
  [535,] 10514  6477   472 10197 12668  4208  4786  7286   654  9582  2344
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  [538,]  6638  7290  6048 12942 13187  8730  4185  9264  3474  8381  1690
  [539,]  9612 13149  6138  9993  6661 13243  5920  7486  1864  2575  9558
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  [545,] 11144 10100 13041  6745 12254  7428  5304  6247  4240  6059  5653
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  [569,]  8774  4058  2379  1799  8729  8134  7273  2779   642 11807  1182
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  [577,] 10885  1988 11874 13044  8413 13313 10196  4958 10021  9047 11631
  [578,]  5410 11726  8560 10206  5752  6288  1726   448 13089  2467  9980
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  [588,] 11218  9441  6143 12323  3957  5341  6996  7247  3974  5218  5635
  [589,]  8878 10352  2611  5292 12420  6397  8511  7439  3666    99  4140
  [590,]  2485 11144  2020 11032 13543 10818  8810  6342 12047 11293 10837
  [591,] 12702  2378  3223  7012 12290  3569  8754 12866  4269 11810  8660
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 [1222,] 11960  6531  2396  8410  2087  2154  9540  2920  3630  2634  6149
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 [1226,]  4848  5731 13535 10283 10939  9355 13385  6081 12713 12131  9420
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 [1235,]   843  9463  7166  7248 10809  3285  5363  6578 11980  2282  1205
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 [1243,]   670  7809  6491  2943  2857  4042  5505   410  5686  7659  1331
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 [1253,] 10379  3079  6122  7849 11754  5384 13302  8525  4314  7214  2879
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 [1255,]  6179  8142  7390 10035 12195  6814  7747  6200  5284  6037  8929
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 [1260,]  1548  7134  6942  5092  7542   128  4114  4248  4206  2156   772
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 [1262,] 12199 10706  7108 11719  8033   699  9140 10629 11245 11696 11677
 [1263,]   737  6427  4621 11088  1362  8936  1367  2236  6082 12332  8832
 [1264,] 13316  7445  5952  7792  4476  3426  4537  4581   641  2370   335
 [1265,] 12822  4253  5992  5132  9683  3654  8286 13478 10120  3948  9624
 [1266,]  9470  3968  7363  2005  4655  9956  4137  1974 11191  8068  4838
 [1267,] 12522 13443  8671  2020  6233 11886 13345 12989  9935 12549  3521
 [1268,]  8502 10852  7051  9632 13144  7401 11865  9878  8534  8216  5551
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 [1722,] 12636 12430  6301 13626  9460  9706  8390  4255  9488 13250  8819
 [1723,] 13287 12874 13151 11503 12852 11968  6858 11606 11555 13571 10971
 [1724,]  3509  9259  9083  1858   189  4265  4925  7554  2896  6315   221
 [1725,]  7463  9233  7121 11465  7574   726  4564  9404  7005  8531  6590
 [1726,]  9205 12301 12224  7622  4269  2880 12777  3091  1148 13403  8329
 [1727,] 10811 13405 12644  3563  4245 11169  4559  9671   984  5149 12174
 [1728,]  5236 10047  7366  2684  8595  6531  7146  3397  6297  5826  7906
 [1729,]  1765  3147  1656  7882  1401  6823  5881  4284   453  3030  9484
 [1730,]  1668  3618 12644 13048  1811  4234  5688 11127  8361  1446  2744
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 [1732,]  2184  6902  6940  4077  6748  9506 12730  1247  2220  9128  8390
 [1733,]  4346   818  2135   724  1205  4031  1583  3068  2781  2657  3331
 [1734,]  6180  8146  9259  6124 12362  5060  8639  2517  2490  8211  5949
 [1735,]  8531  7401  2412  3568  7595 13097  9714  9941  4233  7104  1626
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 [1738,]  9366  5924  7790  5731  4810 12898  2676  7875  3249  4822  9400
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 [1743,]  7805  6489  6088  6321  4076  8797 10436  8408 12051 11890  5063
 [1744,]  2695 10329   819  7376  2434  6659  4445  2991  4670  4482  1945
 [1745,]  9769  4167  7176  7913 12748  1962  2127  2317 11722 10496   796
 [1746,]  8190 11865 10570  3173  7190  6013  3768  9797 11107 13001  4223
 [1747,]  4587  6707  8589  9567  4751  4377  9837 11903 12875 11954 12042
 [1748,]  5434 10372  6210  2178 12773  5424   696  1663  2031  1864  9170
 [1749,]  7389 11733  4564  5350  1201 10813  6616  5447  1353  5439  5064
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 [1751,]   501 10155  5101  8357  1666 13559  2443  7342  5457 10440  6782
 [1752,]  1378  8998  7738  3104   661  2927  2739  4775  5744  6823  3543
 [1753,]  8996  2637  7216 10941  8331  5628  5578 10918 13136  4525 10475
 [1754,]  2705  5640 11123 10535 10224  9058  8912 12754  8042  5582  8241
 [1755,]  2356 11449  5822  1226  8370  5317  4091  1431 11800  7060  1594
 [1756,]  9356 13115  7843  8317  6669  4866 12218  9848  6095  4280  1082
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 [1758,]  2629 10436  1003  1985 11406   504  1583  1782  9836  2657  1917
 [1759,]  5473  3388  2030  9555  3106 12772  6095  2239  4876  8546  6819
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 [1761,]  8716  9649  5463 11029  1479  2142 10428  5353 10709  8743 12018
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 [1763,]  5184  7856 13528 13640  7361 11648 12075 13514 10312  8950  3484
 [1764,]  9421 13265  2679 10481 11144  2864 12394  6150  8516  3887  8098
 [1765,]  4811  5812 11887  8147  3888  1395  9274  7998 11785 11565  5192
 [1766,]  7587  9400  9429 11058 11178 13496 12825 10824  9577  9416 11463
 [1767,]  4668 11200  3936 10586 12142  1752  4500 12684 10891 10924 13263
 [1768,]  1970  7008 10636 12752  6440  8001 11950  9093 11659  2351 11648
 [1769,] 10392  6360  6002  1532  9722  8070  7636 10847  7514  8244 10360
 [1770,]  7701 11007  4163  3282  3134  2866  3953  5534  1312  3183  2300
 [1771,]  8965  1303 11685 13240  9921 12335 10668 12891 12989 11336 12440
 [1772,]  6533 11750  8530 11854  7619  3972  2423  7292 11962 12934 11953
 [1773,]  8625  7253  9902 11639  6551 12058 12566  8208  4010 10410 12227
 [1774,]  6813  9511  2873  7374   498  1161  3037  2997   350  3505  4157
 [1775,]  3013  8138  5772  2138 11935  8704  1636  4697  2481  3010  2122
 [1776,]  7778  1221  5431  5321  7045  1448  2986 10069  3528  2274  1757
 [1777,] 10207 13119  8597 11568  5199 13513  8906 11036 12189 13478 13449
 [1778,]  9886  5246  3751  9445  5630 11686 11108 10900  6685  3387  7042
 [1779,]  5014  3702  2974  4694  8994   673  4689  3878  4943  3653  2708
 [1780,]  6839   542 13270 10524 10946  6724 12455 13611 10287  5557 12742
 [1781,] 12934  9062  5282  6917 12768  7312  7243 10883  3968  9193  9894
 [1782,]  2307  6775   632  1062  5781 12242 11178  3409  3612  1857   936
 [1783,] 11003  2079  1596 11646  5447 13426  8096  9637  4307  4148 11061
 [1784,] 11930  7309  7369  3319  5172 13487 10560 11356 13105 11133 13127
 [1785,]  6401 12516  3293  1562 11986 12243  9525  9401  2735  8710 10017
 [1786,]  1686   663  2124  5929  2128   424  1382   545  1202 11495 11970
 [1787,]  9502 10979  7948  1459 10427 10442  8021  7261  9185  8362 12237
 [1788,] 12901 13103  9688  5612  5366 13086  5630 13445  8210  8916  3362
 [1789,]  1470  4036 11527  3540  1927  3056  5188   994  3298  5830  7966
 [1790,]  8070  8228  6010 13301  1540  3483  9302  3432 10433  9250 12151
 [1791,] 12422  5520  8406  8478  7678 10891  1726 10730  4349  2429 11944
 [1792,]  8339  9023 10446  8817  6511 12879  4622  9730  3238 10110 12843
 [1793,]  6444  7614  6629 11832  5771  7447  8114 10235 11284  9630 11440
 [1794,] 12151  7820  9718  5037  5905  7234 10964  7007  8084   942 10971
 [1795,]  6999  1037  7272   437  8023  6165  5233  8833  7421  2813  7932
 [1796,]  4836 10849  9208 11328  5159 12958   289  1941 11782  9087  8907
 [1797,]  5476 13279  6169  7284 12465  4757 12740  9990  6593 12647  5626
 [1798,]  6338  1420  1979 11260  6742  7890 13404  7608  8762  4306  2162
 [1799,]  2140 10703  1100  8261  5928  3546  9604  5150  2431  2169  3580
 [1800,] 13281 13549 12913 13055  9944 12475 13453  8801 12991 13522 13709
 [1801,] 11787 11543  3549  1680  7032  2935 10646  9126 10503  5360  7022
 [1802,]  9205  3637 10376 11459  4148  8236  4542  3091 11557  5545  4198
 [1803,]  8548 12112  8106  9768 11760  8701 10872 13458 11875 10268  9546
 [1804,] 13188  8457  6987 12773  4470  1931 12138  1038  7240  4136 10368
 [1805,]  6223  7168 11494  4866  1922 12203 11225 13422  6286  3711  3906
 [1806,]  3721 13011 10429  6522  4755  7010  7913  9548  4683  2069  8431
 [1807,]  9586  1163  3381  7905  2757 13000  7761  7578 11911 11261  4665
 [1808,]  5048 11456 11392  7166 12614 11490  9814 11205 13095  9329  6488
 [1809,]  1175  7572  1667  1691  2393  2955  8466 13534 10685 12983  9165
 [1810,] 10480  5306  4984 11695 10787 10104  8141  2306  4993  3367  9543
 [1811,]  5175  6759 11135 11456 12077 13052  8983  8627 11541  8751  2663
 [1812,]  6029  5787 11335  7160  9305  4698  4870  7073  7000 13240  8495
 [1813,]  2537   851 12843  1984  3186  6715   313   807  2039   836  4126
 [1814,]  4725 12342  9584  6669 10105 13139  7941 13448  6281  9009  8402
 [1815,] 10793 13209 13118  8654 12111 13117 12068 12731  9018 11450 13348
 [1816,]  4578 12340  5643  7675  8242 12783 12469 13614 10774 13176 13602
 [1817,] 10624  4202 11449  8340 11830  9702 13490 13606 11398 10479  7775
 [1818,]  2751 10716 12696  3213 11053  5716 10987  5939  6859 12116 12521
 [1819,]  4047 10018  8264 12055 12203 13198 10505  9876 10391 13245  5872
 [1820,]  6792  4342 11013  5293  3192   666  6235  2820  5693  4447  4104
 [1821,]  9926 11581  8063  9347 11481  8683  2869 12241  4419 11045  2295
 [1822,] 11816 11611 10766 10852  3957  2347  5770  9415  8690  6094  6650
 [1823,] 11064  2212  8310 11334  1441  5032  8658   548  2494  3703 11469
 [1824,]  6615  8431  6023 12915  3939  6939 10228  1085 10609  7121 10453
 [1825,] 11772 13140 13589 10855  5975  1928  9106  1606  2598  2482 11757
 [1826,]  8370  1521  3661  1347  3856  2560  5028  7589  8269  5289 13145
 [1827,]  8073  7812 11276  3592  5340 10375 12176  7944  5887 12627 11677
 [1828,]  7964  8933  8691 10777  8518 11801  7832 10414 13698 13388 10157
 [1829,] 12960  4286 12114  2280 11321 11516  4716 11244 11902  6322  8683
 [1830,] 10465  6427  9458  3946  3108  7351  9160 11887  2276  4229  8086
 [1831,] 12292 10877 13244  5799 10833  8940 11888 10201  8613 10509  8680
 [1832,]  9940  8899 11709 11585  4746  8047  6717  3952  5742  7712 10931
 [1833,]  4141 13268 11057 12855  6505  7801  4444  6904  1841 12925  7996
 [1834,]  6135 11879  9643  5644 11053  3588   898  8664 12234  9772 13042
 [1835,]  5916  9950 10473 10825 11744  8742  7512 11125 10413  2167 13407
 [1836,]  4484  9240  7171  5213  8703 10934 12258  1649 10612  7288  2268
 [1837,]  3376  7298  1131  6229  9997 10341  9303  9179  9189  7263  3751
 [1838,]  9002 11967  3863  1510  8568  8128  2833  4048 12326  5682 13370
 [1839,] 13316  4273 12359 10198 11158  1437  5386  4559 10573  1546  3812
 [1840,]  8721  4401  4456  1675 10790  6027  6071  8146  2981 10304  4802
 [1841,] 12262  9375  8463  4914 12464 12178  2366 11412  5327  6003  2460
 [1842,]  6130  9082  3128  4707  7715  7151  9165 11049  3037  3220 10278
 [1843,]  4398 12163  5118  2601   382   414   186  2143    97   188   959
 [1844,] 11867 13371 11658 11832 10619  1608 11557 10147 13606 11096  9074
 [1845,]  9289 12348  7790 10866 12373 11754  8069 10376  7192 10124 11005
 [1846,]   779  8545  2477  3168 13053  2175  7604 10680  7790  5417  8183
 [1847,]  8876 12152  1270  2569  4734   245   424  6459  5674    99  1846
 [1848,]  3366  6700  9407  2253 12775  1644  9569  5374  2048  5441   993
 [1849,]  3286  8679  7543  1130  1487  3015   788  6347  1375  8698  9994
 [1850,] 11674  9039 13212  5131  3892 13645 11745  8068 11865  1504  4452
 [1851,] 13040  8462 13031  8953  6718 11762  9745  2904 13542  4324   527
 [1852,]  8270  9775 10608  6069  9287  3627  4847  1386  1450 10053  7417
 [1853,]  8169 12384  4824 10266 10314  9769  5162 12472 13232  4552  2730
 [1854,]  3099  3858  9214  8271  8556 11535 12302  5107  4164  5937  4027
 [1855,]  8355  7973  9702  4958  9542 12276  2748  4838 11145 13345  8376
 [1856,]   217   405   848  7982  7978  3843   743  1305   793   243  8003
 [1857,]  1338  5631 11537  6470  6791  7824  3920  2284  9271  9434  8983
 [1858,] 11553 13408  6659 11487  7176 12823 10759 12715 12166 12788  3409
 [1859,] 12071 12607  6657  6567 13583 12850 12970 11680 13695  6634 12472
 [1860,] 10687 10338  2769  4316  2831  6655 11158  2965  7899  4409 10023
 [1861,]  8998  7769 12964  6494 11575  5633  2569  8684  7947 11527  3381
 [1862,]  6737  4170  3395  8337 13179  5441  1515  2938 11370  3138  6782
 [1863,] 11910  5273  4995 13358 10782   323 10228  4529  2107  5976 10454
 [1864,] 12354  9441  5183  3649 13160 11198 11001  8226  9181  6113 10385
 [1865,]  8340 10714  9646  7769 11127 11406  7509  6741 11839 12127  5431
 [1866,]  6571  7691  8522 12859  5536 12063  2784  6552 11277  3300  6020
 [1867,] 10830 12884  3128  7600  7283 10511  6865  9551  3792 11830  6478
 [1868,]  2537  8676  1448  6380   780  3994  1738   857  7858   844 12732
 [1869,] 12953 10385 13094  4917 11165 12567  9097  7242  5997   443  6874
 [1870,]  6402 12803 11671  3165 13421  5213  4327  3535  9809 11938 12019
 [1871,]  9578  8428 10733 10000 10618  6258 10646  7575 11247  3406  6726
 [1872,] 13364  3136  4122  6169  4487 10676  5322 12216  2630  8492  9626
 [1873,]  7937  9668 11120 13414  5156 12776  8896 12600 12101 11377  9189
 [1874,] 13070  4395  8517  7445  9674 12975  6575  9344  4459 10372 10794
 [1875,]  6164  8162  8889  2541  7811 12632  6660  6157  6581  4004  9433
 [1876,]  4689 11341  9147  3799  4746  9445  7932  4850  1015  4755  3837
 [1877,] 13448  3385  7420  6229  4492  1442  2171  3546  2180  8438  9806
 [1878,] 12844 13460 13501 12734 12623  6843  7826 12062 12930 13482 13216
 [1879,] 11520  6778  8809 11538 12586 11286 10190  4043 11587 10800 11592
 [1880,]  8708 11107  9362 13140  4954  6172  8692 11764 11963  9574 11925
 [1881,]  9726 11651  7975  6307  4069  7612  8495  9321 12037 12373 13587
 [1882,]  2955  4841 10520  7823 11448  6065 12597 10394  9269  2490 12179
 [1883,] 10685 10246  4653  7273 13526  9005  6539  6576 12016  8467 10789
 [1884,]  7389  2828   629   406  2370  9847 10437   661  5600 10574 12421
 [1885,] 10217  4935  4891  9924  6696 10099  7610 10395  1761  8210  8454
 [1886,]  4146  9281  6051  3617  3929 12597  4161  9041  5300  9350  4519
 [1887,]  9962  5043  5248  6985  9478  1784  2002 10466  7088 13485 11290
 [1888,]  3729  9782  4843 12176 10260 12823 10762 12984 12202  2741 13466
 [1889,]  5457  1864  8567  9166  6870  5213  5519   455  5706   876  1412
 [1890,]   843  4296  4278 12004  1648 12753  9481 12254 11050  1783 10454
 [1891,] 12864 13554  8655 10623 11509 11127  7908 13277 13146  4653  5357
 [1892,]  7281  9109 12281  4654 12234  4946 12378 13151 12344  4708  3562
 [1893,] 11675  9851 11865 11175 10330 10885 12237  9782  8475  5851 10996
 [1894,] 11307  6439 12773 11979 11313 11377 13066 12868  7250  3300  7777
 [1895,]  1478 12688  2329   173  2203    65  6349  3325   473  2145   199
 [1896,]   842  1877  3588 10515  7918  7897  8394  3825  1330  5350  9022
 [1897,] 11782  9277  6177 10847 11240 10540  7016  8202  8588 11231  8636
 [1898,] 10466  7694  2891  1646 11930  4508  4708  2337  2302  4350   894
 [1899,] 10038 12405 12638  9805  4405  9647 13186 10370 10410  3871 12179
 [1900,] 11330  5497  3784  4407   980 13598  7695  6667  4458  5314  9015
 [1901,] 11111  9412  5143  2791  9580 10907 11527  5605  1469 12244  7669
 [1902,]  6397  3385  4635 11835 11794 11087  8297  1505  3871  8261 12603
 [1903,] 11873  7426  2438 12301 12326 11094 13062 12164  9684  3929  9545
 [1904,]  7112  1358 11332  8222  8082  9550  7136 10559  9135  1462  2140
 [1905,]  4692 13605 11175  7541  2172  8280  9994 11125  8115  2880  9365
 [1906,]   456  6181  2411 10185  7595  4485   363  5298 11882  6247  1136
 [1907,]  5948 11107  2829  2453  6344  6087  3865  6524  9205  7399  3150
 [1908,] 13236 11576 11589  8325  9106  3731 13030 10893 11025  1775  7035
 [1909,]  5951  4978  9793  6100 10230  3546 13428  7120  1155  5824  3362
 [1910,] 10793  5828 13398 11603 12921 10391 12888 13611  9002 12466 11588
 [1911,] 11074 10051  8263  5314  5921 13202 12382  5101  9462  3844  8909
 [1912,]  6949 13600  9570  7541  3774 11277 11422  6792 11504  3649  5358
 [1913,]  4904  6066  3097  5082  5273 10236  3114  5184  1735  3843  4517
 [1914,] 11585 12857 13134 12691 12928  9878 12923 12048  7984 12840  6344
 [1915,]  7976  7781 13494  1431  8373  3417  2569 12334  5826  6713  9281
 [1916,]  3594  5639  5693   751  8994  2087  5930   567  5736  2697   287
 [1917,]  9798  6397  5960  4163 12282  8517  7182   727 10121  3254  3726
 [1918,]  9370  2946  6062 11247  7544 12647 12822  6136  4418   731  7523
 [1919,] 13129 12853  9567 13532 12896 11406 12503 13488  8376 11530  8406
 [1920,]  9138 10596  8725 12209 12169 10512  3814  5760  9104 11550 11069
 [1921,]  5002  2020  9138  1759  4350  3725  2941  1922   440  2056  6857
 [1922,]   638 11598  6122  7873 11149 13387 12824  4526  8577 11038  9394
 [1923,]  3815  1505  7513   516    67  7468   525   968  1938  6006  5908
 [1924,]  3880 11358  6795  1680  4808  8618  9199  8876  8518   403  6535
 [1925,]  7497  5297  7944  8702  3053  7017  3569  1579  4809 12644  7615
 [1926,]  3165  2023   643  5711 10110  1539  3587  7705  8197  1350   449
 [1927,]  8552 10454 10163 12833 10663  8580  4704  9097 12389  8512  8846
 [1928,]  6510  9592  9321 13646 13372  9662  5288  9049 12768  9562 12929
 [1929,]  5640   843  6630  6469  8183 10042 11106  7628  6163  9661 12409
 [1930,]  9786 10416 10977  4193 11904 12764 11727  8296 10641  8438  6899
 [1931,]  8119   972 11146  6549  5267  8559  6309 11905 11750 10646  5159
 [1932,]  9265  2689  3090  4040  1583  2561  6333  1386  2347  2821  1041
 [1933,] 10866  5774 11219 12182 10270  9731 13548 13656 11764 13405 13049
 [1934,]  9154 10772  2230  5696   712  9666  7586  7938  9532  9482  9458
 [1935,]  8282  5819 13353  2130 10378  4444 13211 11644 12322  9880 12061
 [1936,]  9863  5555  6617  1406  1479   786  7430  2254  4675 10548  6164
 [1937,]  3699 13430 10446 12206 10260 13522 13382  6936 10013  9207 12202
 [1938,]  6808  5620  8567  5405   389  4034  5142  1294  2783  2647  3330
 [1939,] 12988  5254  5160 11660  1632  4181  1675 11217  4393  9585  6579
 [1940,]  6529  9384 13373  7797 12719  5110  9733 12163  9687 10287  4602
 [1941,] 13105 13206 12641 11525  8407 10282 12930  7745 10043  9195  7493
 [1942,] 13182  2423  8908  5599  4918  1922  3569  2865  2901  7247  9536
 [1943,]  1401 11790 12928 12844 13120  3764 13531 13146 11599 12058 10971
 [1944,] 12343  8296 12353  8758 10796  9571 10059 11748  7045 11676 12863
 [1945,]  4719 13386 12553 10602  9206 10360  5685 13543 11489  7783 10841
 [1946,]  4455  4158  1167  5116  5583  2604   618  8328  2922  1693   132
 [1947,]  7435  3998  1331  3933  6429  9939  1383 12095  5954  4600 12257
 [1948,]  7046  7837  7770  4958 10884 11173  5931 13329  6886 12440  6266
 [1949,]  7860 13529  5458  2464  5542  5136  1522  4452 11060  2394  8888
 [1950,]  8646  4543  6562  4931  3308 11678  3964  1697 11054 10330  3992
 [1951,] 10430  9367   731  9890  3493  5672  4377  3646  6427  7101  6610
 [1952,]  3972  7963  3770   504  1832  8463   980  5639  1070  7758  9893
 [1953,]  4578 12677  6659  7676  9216 13086 10712 13614 12313  7779 13450
 [1954,]   337 10352   716  3381   504  7641   424  5481  1392  1319 12727
 [1955,]  9950  8761  5683 10586 12899  9107 11947 12679 13628  3672  9377
 [1956,]  5183  7896  2275  4968  9386  7760  3703  3937 12204 10757  3430
 [1957,] 11616 11294  6929 11934  5329 12037  6040  7076 12312  4808 12204
 [1958,]  7611 10144 13023  8705 12273 11043  4197 13047 13071 10995  8644
 [1959,]  5878 11854  8816  5503  9055  8282  6002  4037  5097  8972  3405
 [1960,]  1321 11037  1853  2921   222  1132 11185  1692   606  5466  2499
 [1961,]  3122  1009  3516  7358  2424  4298  9651  1999  3639  4377  3290
 [1962,] 13048 10091 10705 11282 12319 12132 11108 13474  8763 12299 10460
 [1963,]  9429  6157  4399  7408  7854  8646 12683  1976  2472 12153 12407
 [1964,]  5682 10110  1828  9452  3140  1688  1005  2261  3141  8530  1704
 [1965,] 11067   636   847  3803 12198  7420   743  3185  2436  1489  4818
 [1966,] 12198  1581 12767 13547 12373 13635 12802  9925 11235 12695 11024
 [1967,]  8223  8843  8781  7119 12847  7060  8199  3285  9118  2768 13685
 [1968,] 11617   870 12337 10233  8075  1810  8229  3308  5866  8051  5340
 [1969,] 12854 10665 11179  9797  9931 12427  9013 10365 12923 12121  5361
 [1970,]  1508 11372  3115  6171  2729  5846  1515  6043 12251  3823  1084
 [1971,]  3084  9951 12015 11895  3009  9197 12243 11174  7369  5801  9779
 [1972,]  5864  4665 10411 12132 10129  8313  6875 13561 10773 12788  9210
 [1973,]  8363  6167  7106  7876  1868  9662  5524  7141  9589 10244  4382
 [1974,]  8223 12303 12678 11861  9054 12619 10461 12122 13511 12137 13709
 [1975,] 12033  4665 12228  8989  8354  9779  5157  4903 11080  8948 10174
 [1976,] 10574 10241  1128  6250  4491  3600  7171  6489  2895  4063  7788
 [1977,]  2915  7937 12973  7721  5853  5609  9869 13335 12969 10833  6205
 [1978,] 12668 11586  9940  2372  9595  5111   916  9376  3383 12218  1233
 [1979,]  7113  5890  4371  1205  9417 10820   605 11172 13232  6667 10556
 [1980,] 12342  8296 12749  3620  9110  4404  8664  6317  5403  2254  9578
 [1981,] 10631 11724 13081 10406 12749 12067 13041 10894  4036  6452 12405
 [1982,]  6792 10476  7513  9487  7132 13245 13503 11406 12866  9720 13586
 [1983,] 10338  6098  7362  3898  9841 12746  8637  4898 12352 10031  4838
 [1984,]  7908  5563  5547  8467  2527  2722  9457  6648 10265  2490  3992
 [1985,]  7671  3450 10271  8015  7128 11559  3357  8148  6785  5471  6100
 [1986,]  4313 11700  9101  3788  4081  2340  1696  5373  3630 10573  5142
 [1987,]  5072  4764  7220  8183  5623 12407 12707  6986  6011  8789  8003
 [1988,]  9385  9181  5566 12854  9550  2311  8084  5568 10509  4229 11994
 [1989,] 12702 13376  9959  6660  9566  7778 10872  5550 12371  5249 12220
 [1990,]  4526  8696   580  5242  6054  8504 11132  4736  4514  4345  5978
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 [1994,] 12077  3615  7724  4495 13120 12825 12055  3889 10893  5741  9299
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         [,45] [,46] [,47] [,48] [,49] [,50]
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    [4,]  2639  1412  4138  5061  2831  2524
    [5,]  5479  1939  2331  6093  4938  4957
    [6,]  3408  8178 10795  6228  8812 11734
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    [8,] 12618 12470  2939  7540 12023  1964
    [9,] 11766 11229 12428 10920 12412  5222
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  [381,]  6432  4620  8863  7658  8918  2578
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  [396,]  9329  6893 11791  6951 10230  6823
  [397,]  8411 13285 13147 12784 10541  8368
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  [400,] 13202 10450  1863  1822  4486  8245
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  [403,] 11985  3935 12203  1617  6680 13576
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  [411,]  4518  1968 10154 10730  2911  6416
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  [413,] 11677  1606  1975  6003   351   732
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  [430,] 11131  5688  6493  4736  7096  3638
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  [433,] 10063 11384 10987 13129 11577  5744
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  [509,]  8609 10519  7894  7308  4208  4066
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  [572,]  3623  6168  4150   680  7564  2626
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  [577,]  5949 11540  5349 11232  7089  3739
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  [579,]  4260  9120 12832  7636 12487  5320
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  [581,] 11189  6260  7931  6437 10553 12769
  [582,]   733  2161  4628  6798  5901  1801
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  [586,] 12993   249  2597  7707  9197  9775
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  [600,] 10266 13420  5286 13354  9145 11514
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  [602,] 10215  1081  2744  2654  6408  1576
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  [604,]  2486  6487  6836  5593  7816  6474
  [605,]  1170 10040 12813  6627  4319  8569
  [606,] 11605  8701 13035  9895   199  8993
  [607,]  7979 12505 11657 12197  9203 10618
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  [609,]  3227  1823  5605  1241  1945  6254
  [610,]  5905  7872  6467  6178  2246   715
  [611,]  4229  2849  1807  7067  4780  1808
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  [613,] 13453 12253  8087 12246 10333  4179
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  [615,]  9640 10850  3657  1769  9504  9450
  [616,]  6347  9471  4630 12611  2773  1774
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  [620,]  3929  9895 10535 12819  6529  9402
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  [980,]  6214  9594  7377 11961  6501 10229
  [981,]  8742  4867 10839  5247  3381  6981
  [982,]  5906  7713  6463 10688  5582 10688
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  [984,]  4544  6085  2366  4677  8334  4968
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  [986,]   745 12438  3728  1816   894  6406
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  [989,]  6937  9739 10252 11390  3939 12833
  [990,]  9223 12847  3299  1917  2973 13465
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  [992,]  2645  2093  1813  8610  3406  4473
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  [994,]  8460 10883  6805  6836  3714 11168
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  [996,]  2838 12514  8401  7977  8187  6788
  [997,]  7862  2938  1813 13431  6348 10410
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  [999,] 13300 13440  9875 11743 10124 12132
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 [1001,] 12466 13470  4192  8789 11590  5546
 [1002,]  7979 10349  2546 12197   199  5543
 [1003,]  3804 12006  6448  9024 10836  6686
 [1004,]  7832  9313  4015  1004  4381  2504
 [1005,]  4328 12939  6690  7444 11314 13040
 [1006,] 10912 13098  6572  5183  7330 12887
 [1007,]  1365  3813  9192  4906  6115  4182
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 [1009,]  5023 10057 10445  5956  6926  2315
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 [1012,]  7703 12282 12848  7291  6267  3794
 [1013,] 12016  2510 12063  6102  4882  5964
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 [1019,]  4462  2765  1815  6797  9336  7381
 [1020,]  1285  7233  2322   765  2489  1669
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 [1022,]  4650  7124   182  4101  6588  5220
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 [1025,] 12396  2872  5034  9591  8884 13576
 [1026,]  3176  6239  6654  5055  4802 12345
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 [1030,] 11485  8443  8382  7737 12959  5629
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 [1035,]  3856  1160  8190  6613  5307  1718
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 [1037,] 12979  8158  4955  3885  9266  4163
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 [1039,]  2553  1925  9062 12187 11629  5759
 [1040,]  7464  9061 13500  9118  4873  9558
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 [1042,]  3326  1518  9765  8482 10570  5375
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 [1048,] 10571 11630  9909  9820 13267  4734
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 [1050,]  1207  4301  3005  4369  2288  4453
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 [1053,] 12958  9357  3939  3358 11960  5050
 [1054,]   548  7059 11538 10142 10441   137
 [1055,]  1620  6712  6611 12425  7410  7005
 [1056,]  9006  7502 13304  7986 11615  9773
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 [1058,]  9436  9923 11877  1667  1872  6251
 [1059,]  6629 11796 12919 10129 13485  8439
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 [1061,] 13219 13293 11015  7730  1823  4543
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 [1063,] 12999 10619  5219 13095  6947   965
 [1064,] 13169  3737  7235 13573 12698  2575
 [1065,]  1277 10927  3051  7147  9431 10954
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 [1069,] 10602  5953  6967  3345   105  3779
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 [1072,] 12413 11373  9330 13618 12970  8810
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 [1074,]   814  3279  4768  8583  7840  5538
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 [1079,]  7966 12514  4164  8046 10924  5608
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 [1083,]  8160 13563  9515 10760 13067  3926
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 [1090,]  8790  5984 10971  4374 11922  8671
 [1091,]   150 13128  1098   576   623   343
 [1092,]  6568  3272   509  3730 12922   964
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 [1094,]  5625 11065 10104  7050  8347  2471
 [1095,] 13228  9456 12226  6922  6898  7774
 [1096,] 11339  3809  7026  9851 10928  8844
 [1097,]  2967  3103  6397 10137  9599 11609
 [1098,] 12210 11871  1497 12269  5664  8448
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 [1102,]  6208 12448  8504 12997 10517  8336
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 [1104,]  7092  8579  4353   540  4904  4875
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 [1107,]  9627  4231 10676 10291 12514 10527
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 [1109,]  1521  4527  4525 12487  8847  6159
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 [1111,]  4592  9206  9238  9394  8992  5391
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 [1113,]  5670 11785  7246  2926  4418  2683
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 [1116,]  2969 11738  5978  4303 12777  6988
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 [1121,] 12832  3407  3879  8362  6211  1052
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 [1123,] 12888  3020  3747  1986  7552 11293
 [1124,]  3508  2093  1738  6567  1708 11789
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 [1139,]  2500   227  2249   702  5439  4452
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 [1194,]  4258  9124  9792  4168 12868  6383
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 [1196,]  6144  6734  2682  9989 11714  2325
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 [1198,] 10167 13085  2741  4510  5339 10234
 [1199,]  7181  6791 13064 11461  7703  1745
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 [1201,]  6186  6325  3546  9208 12746  8088
 [1202,]  9277 11324  5477  4534 12914  5120
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 [1204,]  3556 11752  6131  7187 11110  4307
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 [1206,]  9848 10203  3147  9994  7871  8557
 [1207,]  7819  5027 10762  6650  8968  1954
 [1208,]  6085  3234  1360   232 12896  8421
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 [1211,] 12297  8675  5764   689  7615  9693
 [1212,] 11804 13157 12402 13269 12486  8613
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 [1214,]  8597  8039  2824  5418 11922 12753
 [1215,] 10645  5039  2368 10164  4448 13167
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 [1222,]  4384  1644  3827  9458  6409  5518
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 [1225,]  6043 13275  3548  1318 11354  4035
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 [1233,]  5110 10011  5886 12990  7386  5843
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 [1235,]  5531  5041  6095  8404  2546  2618
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 [1260,]  1153 10276   822  9121  9396  4272
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 [1262,] 11925 10287  9971  6234  9615 10813
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 [1266,]  8840  7271  4109  7185 10348  3304
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 [1268,]  5818  8818  8411 11381  7384  9025
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 [1274,] 12316 12668  9075 10548   409 10832
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 [1280,]  6559  2374  6864  1495  7852  9734
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 [1283,] 13341  7767 10980 11243 12176  7905
 [1284,]  9148  3422 11113  3804  9252  5727
 [1285,]  6435  1506 11920  3506  7356 12753
 [1286,]  5392  5770  9819   122  2945  7528
 [1287,] 13383  3849 10044 13412 12354 13367
 [1288,]  6441 11608  2797 13381  2208  6969
 [1289,]  2605  5049  1727   753  2506  2408
 [1290,]   960  8518  7476  9215 11807  5825
 [1291,]  9930  9809  7353  9625  7019  3637
 [1292,]  2828  4117 11124  9237  8528 10775
 [1293,]  1254  5947  9125  3374  5156  7171
 [1294,] 11066  8928 12372 11401  7532 11591
 [1295,]  7790 10290 11617 10243  7770 11214
 [1296,]  9595  5329  2862  8557  9801  3504
 [1297,]  6582  7063  4804  2414  7382 10679
 [1298,]  2361  9907  4553  6782  1942  5233
 [1299,]  1896  8382 12597  1973  3415  9431
 [1300,]  9150  2537 10378 11630  4473  9789
 [1301,] 11826  6991 13116  9599 13667  7638
 [1302,] 10298 11399  3445 11952  8589 13543
 [1303,]  1462  8724  1273  2411  3594  8969
 [1304,] 12224 12141  5703 13647  9424  7511
 [1305,] 10077 10561  3416  9962  9137  9756
 [1306,] 10800 13105  3475 13319 10021 11494
 [1307,] 13108  4025  7784 10250  9702  8712
 [1308,]  1876  7161  9938  5947  6083  9238
 [1309,]  6218  4077  1958  9215  5031  9167
 [1310,]  2908  9538  9572  4160   970 10143
 [1311,]  8563  7978  3657 10292 13667  9653
 [1312,] 12113  5548  1413  9720 11579  1501
 [1313,]  9370   677  9464 11988  2978 12618
 [1314,]  6826   811  6032   664  2484  3308
 [1315,]  7876  6168  8343 12508  2411  7668
 [1316,] 13589  2691 13306  9817 11753  2168
 [1317,]  4593 11054  7132  7139  3910  5229
 [1318,] 12806  9678  4312  5896  8072 12533
 [1319,]  5706  7284  6095 10288  4469 12400
 [1320,]  6551  3252  4751  9345 11342  1419
 [1321,]  7973  2986  9318 12569 12961 12484
 [1322,]  1238  6206  9254  3590  8775  4497
 [1323,]  6270  7978 10499  7686 11494  3214
 [1324,]  6338 11491  8922  4774  3602 10327
 [1325,] 11277 10923 10716 11725 10105   229
 [1326,]  6627 10272  9033 10102  4382  3977
 [1327,]  9825  9320  9957  5575 13359  6193
 [1328,]  6728 11085  9033  6003  4849  8303
 [1329,] 10975 12054 13569  7234  8528  4700
 [1330,]  9729  7063  3034  2593  6650 13343
 [1331,]  5810  4093  9365 10478 11007 12014
 [1332,] 13266 11242  6749 11860  5960 10385
 [1333,]  4132  1953  4960  1666  7187 12357
 [1334,]  4328  8525 11308  9388 11926 11244
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 [1693,]  4879  3418 12720  9916  5859 12540
 [1694,]  9165  8898 11115  8054  8106  2138
 [1695,]  4196  4638  8922  4060  4866  2514
 [1696,]  6048 12192  9680 10367 12852 10260
 [1697,]  6843 10322  9260  1495  6640 11367
 [1698,]  8900  9273  1232  3520  4390 13280
 [1699,]  1896   578  9181  4277  4145  1620
 [1700,]  2821  8497 12990 13656  9001 10638
 [1701,]  7909  2130   826  1510  1774  2750
 [1702,]  4765  2421  6462  8184  4647  8320
 [1703,] 10753 13230 12632 12808 13680  9672
 [1704,]  8567  4773  6050  4423 13167  8687
 [1705,]  4890  8089  6506  9148  6036  8240
 [1706,]  9639 12182  5622 10954  8704  5378
 [1707,] 12695 12307  9979 10716 12284  7133
 [1708,]  2443  7415  3650  3334  7350  2651
 [1709,]  7936 11356 12310  9624  9004  9211
 [1710,]  7348   237  2798  2652  5212  4862
 [1711,]  7249 10427 13025  7097  6824 12113
 [1712,]  7519  9639  7739  9391  9710 11909
 [1713,]  1021  2388  2539  2591  1041 12897
 [1714,]  9161  9093 13344  5702 10918  3639
 [1715,]  5494  8209 13355  3677  7749  9390
 [1716,]  4258  1357 10956 10299  6575  2573
 [1717,]   867  2667  3864  7295  1114  5041
 [1718,]  6239 11295  3584  8331 12397 11676
 [1719,]  4137 10396  1539 10643  2648 13223
 [1720,] 13582  2651  7794  7464  7360 12414
 [1721,]  3482 13519 12060 10730   984  7136
 [1722,]  5262  6990 13299  9172  9408  6387
 [1723,]  4775 11646 11428 10463 11629  5708
 [1724,]  8883  4859  8255  7442  1741   347
 [1725,] 11304  7065 12093 12357  3381  5843
 [1726,]  5875   316 12530  5723  7040  6684
 [1727,]  5894  7817  3384 12287  3014  2798
 [1728,]  2698  6025  5062  9175  7308  4318
 [1729,]  6215  2406  3438  6306  2975  3848
 [1730,]  5474  5882  2343   833  4962  2930
 [1731,]  8119  6895 12327 11226  5820  8837
 [1732,]  6324  4641  8929  8983  9390  9519
 [1733,]   529   588  2387  1599  7838   766
 [1734,]  4544  8276 10808  2403  9382  6068
 [1735,] 10077  5390  1993 12694  8483  3634
 [1736,]  5925 11198 13608 12175  9252  7960
 [1737,] 10074  4052 12279  9970  7486 12073
 [1738,]  2560  4821  2338  4034  8305 12480
 [1739,]  3432  8212  4782  3754 12166  8021
 [1740,] 10923  7374 10721 11119  4723  6677
 [1741,] 11967 10270 12881 10831  9637  9130
 [1742,]  7836  8384  3258  5537  3352  5489
 [1743,] 11260  7644  5777  3562  9737  6615
 [1744,]  2660  1463  1829   662  3459  8797
 [1745,]  9811  5978  1121  4329  7497  3869
 [1746,]  6353 10121 12945  9728  7113  9503
 [1747,]  8971  6207  1856 13295   841  7803
 [1748,]  1858   951   486   974  6412  1588
 [1749,] 11267  1641  6900  2106 12065  2597
 [1750,] 10975  5603  6487  7234 13084  9031
 [1751,] 11767 11977  3676  8404  8736 11293
 [1752,]  3859  3045 13029  6718  5681  7960
 [1753,] 12437  6553 12215 13117  5749 13559
 [1754,]  5748  9731 13555  8915 10806  6701
 [1755,]  8830  9260  4016  2445  2133  4233
 [1756,]  9536  4685 10099  3481 11933   803
 [1757,] 10380  7965  6753  4787 10999  6375
 [1758,]  8874   948   778 11031 11494  7681
 [1759,]  5548  4774 12201 10329   826  7612
 [1760,] 11242  9117  7283  7505 13679 12438
 [1761,]  8439  3245  1483 11032 11470  8437
 [1762,] 12749  7813 13625 12900  6961 11493
 [1763,]  1292  6012 13164  8983 13060  4764
 [1764,]  1705  9547  8292  1299  2820  5252
 [1765,]  6403  7394  9720  5856  5903  6294
 [1766,]  3892  8921 13540  7246 13343 13563
 [1767,]  4803  9685 12670  7097 11566  8969
 [1768,] 12479  8715 11685 12694 13295 12497
 [1769,]  3088  5468  9454 10086  7332  8080
 [1770,]  3326  3196  2931  1986  8729  6490
 [1771,]  9919 11836  8447 10417  1831 11391
 [1772,]  1040  9896 10523  9566 10673  6185
 [1773,]  4814  3449  7703 11934  7485  2193
 [1774,]  5663  1424  4989  1490   111  1427
 [1775,] 12573  6742  9090  9108  4867  3104
 [1776,]  9559  8659  3697  4511  9908  7663
 [1777,]  5763  9691 10287  3896 10813  8860
 [1778,]  8876 11070 11618  9442  5378  4424
 [1779,]  2557 10981  3854 11115  9359  2921
 [1780,] 10813 11847   539  6755  4487  2779
 [1781,]  1563  5680  4359 10714  8350  8309
 [1782,]  1510    41  3534   815    71   658
 [1783,]  3797 10571  8484  8256 10368  8966
 [1784,] 13511 11320 11606 10253  3234  9663
 [1785,] 11672  6950 10513  3438  2282  4858
 [1786,]  3455  4975  1672   857 11075  4945
 [1787,] 10187  5282 11838 12770 12802 13480
 [1788,] 13650  6599 12714 11088  4529  8884
 [1789,]  7752  6031   526  3268  2078  6392
 [1790,] 11608 13255 12688 12689 11115  7969
 [1791,] 11977  6061 10870  2860  5353  5054
 [1792,] 12103  1529  9022 13348  9257 12524
 [1793,]  5180  7258  2334 12104  4280  9346
 [1794,] 11719 10083 12159  9877  9272  8485
 [1795,] 13024  9536  7352  1257  9408  7093
 [1796,]  6351 12143 12795 13500  7257  6396
 [1797,]  9562  6342  5879 12432 10528 13037
 [1798,]  3640 12324  6161  3530 12568  1238
 [1799,]  5278   976 11926  5008  6834  5132
 [1800,]  9934 11178 13130 13477  8177 10605
 [1801,]  3081  5267   990  4261  7669  2390
 [1802,]  5945   803  9070 12908  8117  6727
 [1803,]  5693  3848 12552  6276 12353  5858
 [1804,]  9380 10695 10321 12992  8589 13629
 [1805,]  3774  7914 12748  2498  8396  1594
 [1806,]  1254  1875  8099  9897 10121  7874
 [1807,]  5110 13434 12938  3374 11872 10860
 [1808,] 11761  5700  2150  5351  4086  5237
 [1809,]  2193  1643   960   610   440  1725
 [1810,]  5127  3065 12980 11989  5020  8149
 [1811,] 12660 13331  7979 12618 13545 12135
 [1812,]  9458  3552  5561  4777  1398 11189
 [1813,]  1342  2114  6141  6557  6706  1408
 [1814,] 10872  9784 13526  5746  3689  8888
 [1815,]  8998  6641 12213 12144 13398 12821
 [1816,] 10832 10604 12643 12157  6742  7851
 [1817,] 13284 13227 13364 10927 11934 12412
 [1818,] 12528  9911 11781 11676  3521 11414
 [1819,] 11759 12102 13088 12317  3829  4276
 [1820,]  3390  2368  4733  5336   306  6593
 [1821,]  5378  5111  7865  4377 12820  9612
 [1822,] 12951  4928  9119 11984  3432 13653
 [1823,]  5274  3913 10154  2497  7255  1898
 [1824,]  3313  5109 13298  7421  9514  8593
 [1825,] 13648 11224  4298  8369  7425  8153
 [1826,]  8533  1021 10564  1515  6437  9316
 [1827,]  9175  8029  8563 10768  7385  3627
 [1828,]  9032 12776  5171  6897  5713 10708
 [1829,] 11070  8923 12776  4204  8688 11753
 [1830,]  5480  4828 12103  8333  6460  4087
 [1831,]   882  6137 12881 13192   528  9130
 [1832,] 10784  7497  9352 13101 11528 10724
 [1833,] 13309  3864  8059 10356  6729  8259
 [1834,]  8172 11414 13602 12151 10252 12123
 [1835,] 11520  5594  4396  5020  7064 10763
 [1836,]  6769 10163 12627  3526  4386 10426
 [1837,] 11175  5117  2824  1979 12419 11238
 [1838,]  3827  8064 13054  9635 11562 11545
 [1839,]  3938  2179  3352  8396 10391  8116
 [1840,] 10991  6412  8676  4507  7724  6144
 [1841,] 11000  8627  9382  9234  9804  3130
 [1842,]  8329  9842 11082  7240  9553 12550
 [1843,]  1805  4312   716  1049  1084  1411
 [1844,] 12344 12680 12929 12781  6498 13662
 [1845,] 13494  7684  4225  9104  6788 12480
 [1846,]  8277  2528  9662  3438  4126  1066
 [1847,]  3580  3979  6181  4460  9753  8732
 [1848,]  1278  2953  6007  4629 12062  5097
 [1849,]   712  3495  7713  3696   762  1134
 [1850,] 13501  9505  3643  6030 11011  4194
 [1851,] 12578  3296  1490 11996 11155 12206
 [1852,]  9443  2573  1504 11149  5931 11831
 [1853,] 12376  8231 12904  2994  8259  3738
 [1854,] 12886 11552  7854  6086  2833  2476
 [1855,]  9771 12350  8042 11794  4938  2184
 [1856,]  3053 10453  3069   188  4907  3111
 [1857,] 11412  2816 12593  7700  6682 11039
 [1858,] 13297 13328  9902 12198  8141  5548
 [1859,]  5950  7380 13052 10478  2721  9803
 [1860,]  8897  7337  6061  2779  5471  8774
 [1861,] 13603  3313  6205 11673 10017  4584
 [1862,] 10709 13006 12959  8458  2480 10465
 [1863,]  5375 12803  2824  6375  9514 13407
 [1864,]  7850  9176  1649 13030  4012 13181
 [1865,] 13464  2840 10793  2975  8325 13308
 [1866,]  3854  7920 13424  7703  9801  3925
 [1867,]  9131 10655  9430 10046  6279  7106
 [1868,]  2496  4298  3844 12478  4345  1998
 [1869,]  4950  6804  6352 13435  9808  5019
 [1870,] 10222  1863  7702  4624 13206 12690
 [1871,]  7306 12877 13064 10806  9637  9128
 [1872,]  8547 12128 10585 12458  9726 11289
 [1873,] 11543  4354  8443 13112 11508  6685
 [1874,]  6525 10846  2859  2909 12847  6565
 [1875,]  6424 12182 12436  4097 10561 12366
 [1876,]  5804  4124 11003  4967  5857  3927
 [1877,] 12902  2647  5595  7609  3264  4384
 [1878,] 13631 10597 11667 13456 10861  9915
 [1879,]  7048  3563  5428  4736 12633  7801
 [1880,] 11004 13090 12135  8573  7732  6149
 [1881,] 11248  3233  9860  3474  7617 12446
 [1882,]  7216 10427  9475 13186  9633 11527
 [1883,] 11974   322  7202  7458  7914 11950
 [1884,]  1006  8688  1934  7240   712  1036
 [1885,]  9325  3041  5294 11320  1838  7876
 [1886,]  2955  8478  3563 12355  5067  5905
 [1887,]  3777  5450  8467  4151  4647 10954
 [1888,]  9023  3644  8089 12240 12658 12020
 [1889,]   252  4288  7688  1566  6612  1758
 [1890,]  7865 10162  4060  4412  5562 11872
 [1891,] 13196  8846 13035 10471  9189  5639
 [1892,] 10066  3427 10396  7972 11706  6851
 [1893,] 12720  3707  9033 12653 12223 13248
 [1894,]  4320 13430  8834  8426 11338 11213
 [1895,]   261  1500  6681  1241  1944   795
 [1896,]  4604 11787  1220  1614  4414 12379
 [1897,] 12732 10290 12571 10834  8664  3189
 [1898,]  4051  6620 11856  1572  2329  4114
 [1899,]  3785 11395  9429  3158 10970  5668
 [1900,]  1177 11535   690  2903  7755  6575
 [1901,] 11328  7063 10818 11953  2531  5885
 [1902,]  4949 12171  9633 10365  3219  5065
 [1903,] 10186 11583 10535 10881  6184 13182
 [1904,] 10368  8575 12168  2433  9290  8531
 [1905,]   976 11203 13030 12944  7061  7963
 [1906,]  5903  5390   576   121   430 10846
 [1907,]  3342  9657  2179 10343  1692  5222
 [1908,] 13287 10988 11612 12070 11999  4401
 [1909,]  6384  6961  7939  5892  7989   831
 [1910,] 10787  9785 11685 13656 13390 11455
 [1911,]  6344 11244 13429 13499  5647  8587
 [1912,]  9987 11249 11751 10447 13222 13435
 [1913,] 11147 11497  4654  4090  2616  7481
 [1914,] 12938 12671 13451 11737 12172 11561
 [1915,]  3759 11987  3448  6908  5677  3614
 [1916,]  3683  2179  7297  4673  6838  5691
 [1917,]  6520  4004  5683 10275  8644  8667
 [1918,]  1729 12609  3691  7402 11305  8559
 [1919,] 11543  7825 10396  7766 11627  5639
 [1920,]  7079 12047 12720  7024  7004  2095
 [1921,]  6331  4614  8856  7831  6010  4170
 [1922,]  5501  8331 11488 13205  6197  9030
 [1923,]   758  1029  1021  2454   294  1834
 [1924,]  7239 10453  9551  9104  9118  5717
 [1925,] 10174  6249  5445 11449  4009 13338
 [1926,]  9713  3713 10752  5831 13543  2936
 [1927,]  9411  7798  7480  2175  6463   774
 [1928,]  6230 12528 10845  2838 13152 12279
 [1929,]  8953 12276  9291  2936  7888   579
 [1930,] 11401 11772 13208  1544 12483 13052
 [1931,]  5873  3426  5185 11661 11577  2779
 [1932,]  3225 11163  3745 10513   898  6251
 [1933,] 13002  7778 11668  8048 12990 13580
 [1934,]  4876  2164  8612 12286  5062 10808
 [1935,]  8315  4128 12215  9812  9102  8981
 [1936,]  7910 11128  6130  8607  7848  7721
 [1937,] 10119  9470  7559 10667 12671 10778
 [1938,]  5420   357   162  1584  9958  7330
 [1939,]  5527  3836  4916  2608 11840  8122
 [1940,] 13648  4468  2798 13591  5104  8174
 [1941,] 12027  6241 12285  8096 10971 11502
 [1942,]  6057  8523  1918  9281  6231 13333
 [1943,] 12765 11437 11396  9866 10950 12643
 [1944,] 13081 11956 11835 13517  9646  8188
 [1945,]  7937  7378 12706 13637  6972  9741
 [1946,]  4271  5797  3776  1463  2987  6498
 [1947,]   533  7058 13454  4151   148  3033
 [1948,]  9096 12655 13440  9679  9186  5599
 [1949,]  9554   776  2914  6590 13164  7567
 [1950,]  8907 13521 13189 10356  6728  9419
 [1951,]  3737  2192  3578  9218  2965  5840
 [1952,]   720  4573    77  7818  5977 11167
 [1953,]  6869  3335  9369 12157  4495 12808
 [1954,]  3393  1084  2989  1396  4162  6637
 [1955,] 13553 10559  9326  8903 10031 11455
 [1956,] 12942  7051 12910  9008 13688 11568
 [1957,] 10405  5249  7904  5988  4663 13231
 [1958,]  9219  2414  5144  9317  2978 12920
 [1959,] 13313 12211  9871 13139  8230  7759
 [1960,]  5682  2098  6015  7390  4431  2999
 [1961,]  9832 11823  3271  3210  3810  4334
 [1962,] 11163 13428 10123 10226  6343 12379
 [1963,]  5286 10230 10967   338  2071  2562
 [1964,]  6647  4859 10975  1429  1238 11964
 [1965,]  2833 13269  1341  7051  2024  7131
 [1966,]  5012  3437 11811 11384 12367 10732
 [1967,] 10354  8434  4958  9750  8224  8488
 [1968,]  9458  6211 10537  6809  1941 12987
 [1969,] 12446 12794 10222  3939  5598  6745
 [1970,]  3198 11221  6688  4072  3644 13571
 [1971,]  5251 11263 11900  4793  7989  7344
 [1972,] 10032 10629 11652  7798  2587 11390
 [1973,]  5053  9326  3112  7319  8616  1000
 [1974,]  2359 11174  4553  5757  8235  3254
 [1975,]  5809  8798  7404 12202 12633 12963
 [1976,]  6501  5114  6690  7410 13125 10425
 [1977,]  8024  7433 10224  6892 12105 13448
 [1978,] 12554 11454  8477  9233 11256 10850
 [1979,]  4512 10179  8198 11734   993  7378
 [1980,]  6067  7567  5475 13417  2193 13153
 [1981,]  7586 12131 10659  3653 11415  4401
 [1982,]  5454  5381  2977  9502 13508  8733
 [1983,]  6698 11751 11464  8211 13058  4957
 [1984,]  5407 11009 11629  8649  8797 10449
 [1985,]  7195  9664   976  9497 13513  5093
 [1986,]  2654 11128  1738  5318 11350  4868
 [1987,]  2331 11504  7918  4753  4541  7352
 [1988,]  9722  4828  9980 11591 11379 11026
 [1989,] 12684  6078 13182 13385  5088  2977
 [1990,] 12289  5271  1589  6532  6548  1352
 [1991,] 13433 10932 12475 13141 10124  6680
 [1992,] 11740  9968  3693  5140  2712  1865
 [1993,] 13178 12511  9539 12136 13524 10600
 [1994,]  3689  9764  2597  2946  5810  3651
 [1995,]  7189  6810  3404 13273 11406  7229
 [1996,] 11109  4810  7216 11886  7222  2576
 [1997,] 10311 12129 12366  1383  1669  9420
 [1998,]  8297  5531 13563 11091 11021  5639
 [1999,] 10101  8844 13252 12898 10913  4687
 [ reached getOption("max.print") -- omitted 18955 rows ]

#getTerminalNodeIDs(rf_model, nhanes)                             
# Print the model output                             
print(rf)

Ranger result

Call:
 ranger(LBXGH ~ ., data = nhanes_train, num.trees = 50, write.forest = TRUE) 

Type:                             Regression 
Number of trees:                  50 
Sample size:                      20954 
Number of independent variables:  14 
Mtry:                             3 
Target node size:                 5 
Variable importance mode:         none 
Splitrule:                        variance 
OOB prediction error (MSE):       0.6272892 
R squared (OOB):                  0.4051867

#plot(rf)

# Grab OOB error matrix & take a look
err <- nhanes_train$err.rate

Warning: Unknown or uninitialised column: 'err.rate'.

head(err)

NULL

# Look at final OOB error rate (last row in err matrix)
oob_err <- err[nrow(err), "OOB"]
print(oob_err)

NULL

# Plot the model trained in the previous exercise
plot(nhanes_train)

# Add a legend since it doesn't have one by default
#legend(x = "right", 
 #      legend = colnames(err),
 #      fill = 1:ncol(err))

#oob.times(nhanes_train.forest)

Generate prediction model

library(lattice)
library(caret)
# Generate predicted classes using the model object
class_prediction <- predict(object = rfn.model,   # model object 
                            newdata = nhanes_test,  # test dataset
                            type = "class") # return classification labels
                            
# Calculate the confusion matrix for the test set
#cm <- confusionMatrix(data=class_prediction,       # predicted classes
#                      reference= nhanes_test$DIQ010) # actual classes
#print(cm)

# Compare test set accuracy to OOB accuracy
#paste0("Test Accuracy: ", cm$overall[1])
paste0("OOB Accuracy: ", 1 - oob_err)

[1] "OOB Accuracy: "

# Generate predictions on the test set
pred <- predict(object = rfn.model,
            newdata = nhanes_test,
            type ="class")

#`pred` is a matrix
class(pred)

[1] "numeric"

#Look at the pred format
head(pred)

            1             2             3             4             5 
-5.480338e-16  8.900000e-03  8.310000e-02 -6.568635e-16  1.253333e-02 
            6 
 4.420000e-02

# Compute the AUC (`actual` must be a binary 1/0 numeric vector)
#auc(actual = nhanes_test$DIQ010, 
#   predicted = pred[,"yes"])

library(rpart)
#Plot the "CP Table"
#plotcp(rfn.model)

# Print the "CP Table"
#print(modelsRF$cptable)

# Retrieve optimal cp value based on cross-validated error
#opt_index <- which.min(modelsRF$cptable[, "xerror"])
#cp_opt <- modelsRF$cptable[opt_index, "CP"]

# Prune the model (to optimized cp value)
#modelsRF_opt <- prune(tree = modelsRF, 
 #                        cp = cp_opt)
                          
# Plot the optimized model
#rpart.plot(x = modelsRF_opt, yesno = 2, type = 0, extra = 0)

# Execute the tuning process
set.seed(1)              
res <- tuneRF(x = subset(nhanes_train, select = -DIQ010),
              y = nhanes_train$DIQ010,
              ntreeTry = 500)

Warning in randomForest.default(x, y, mtry = mtryStart, ntree = ntreeTry, :
The response has five or fewer unique values. Are you sure you want to do
regression?

mtry = 4  OOB error = 0.05358294 
Searching left ...

Warning in randomForest.default(x, y, mtry = mtryCur, ntree = ntreeTry, :
The response has five or fewer unique values. Are you sure you want to do
regression?

mtry = 2    OOB error = 0.05433092 
-0.01395919 0.05 
Searching right ...

Warning in randomForest.default(x, y, mtry = mtryCur, ntree = ntreeTry, :
The response has five or fewer unique values. Are you sure you want to do
regression?

mtry = 8    OOB error = 0.05401388 
-0.008042388 0.05

# Look at results
print(res)

  mtry   OOBError
2    2 0.05433092
4    4 0.05358294
8    8 0.05401388

# Find the mtry value that minimizes OOB Error
mtry_opt <- res[,"mtry"][which.min(res[,"OOBError"])]
print(mtry_opt)

4 
4

# If you just want to return the best RF model (rather than results)
# you can set `doBest = TRUE` in `tuneRF()` to return the best RF model
# instead of a set performance matrix.

# Establish a list of possible values for mtry, nodesize and sampsize
#mtry <- seq(4, ncol(nhanes_train) * 0.8, 2)
#nodesize <- seq(3, 8, 2)
#sampsize <- nrow(nhanes_train) * c(0.7, 0.8)

# Create a data frame containing all combinations 

#hyper_grid <- expand.grid(mtry = mtry, nodesize = nodesize, sampsize = sampsize)

# Create an empty vector to store OOB error values
#oob_err <- c()

# Write a loop over the rows of hyper_grid to train the grid of models
#for (i in 1:nrow(hyper_grid)) {

    # Train a Random Forest model
#    model <- randomForest(formula = DIQ010 ~ ., 
#                          data = nhanes_train,
#                          mtry = hyper_grid$mtry[i],
#                          nodesize = hyper_grid$nodesize[i],
#                          sampsize = hyper_grid$sampsize[i])
                          
    # Store OOB error for the model                      
#    oob_err[i] <- model$err.rate[nrow(model$err.rate), "OOB"]
#}

# Identify optimal set of hyperparmeters based on OOB error
#opt_i <- which.min(oob_err)
#print(hyper_grid[opt_i,])

This mtry took too long to run so I commented it out.

#are there any NA values 
any(is.na(nhanes))

[1] FALSE

#mean(rf) # returns NA
#mean(rf, na.rm=TRUE) # returns 2

Random forest Visualization

print(rfn.model)


Call:
 randomForest(formula = DIQ010 ~ ., data = nhanesshort) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 4

          Mean of squared residuals: 0.05378079
                    % Var explained: 49.62

nhanesshort

# A tibble: 26,193 x 15
   DIQ010 LBXGH INDFMPIR RIDAGEYR DR1TCAFF DR1TFIBE DR1TSODI DR1TSUGR
    <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1      0   6       4.65       44       13      6.4     1426    146. 
 2      1   7.1     5          70      260     20.3     3708    112. 
 3      0   4.7     5          16       71      8.3     1937    137. 
 4      0   4.7     5          19        0     14.3     3289     92.6
 5      0   4.8     0.46       21       10     10.2     2959     77.7
 6      0   5       1.06       16      121      9.7     3090    153. 
 7      0   5       1.22       79       95     30.3     2031    133. 
 8      1   5.8     3.03       59      249      8.7     2006    166. 
 9      0   4.3     1.76       27       39     15.2     4155     76.0
10      0   4.6     1.03       44      218     66       3135    242. 
# … with 26,183 more rows, and 7 more variables: BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSTRSI <dbl>, LBXSAPSI <dbl>

#(rfn.model$oob.times)
#round(rfn.model$importance,2)
#(rfn.model$err.rate)
#(rfn.model$confusion)
#(rfn.model$mtry)    
#round(rfn.model$predicted,2)

mtry you get 4..Number of variables available for splitting at each tree node. mtry had a strong influence on predictor variable importance estimates.randomForest - For classification models, the default is the square root of the number of predictor variables (rounded down)
Importanice:
1. The first measure is computed from permuting OOB data: For each tree, the prediction error on the out-of-bag portion of the data is recorded (error rate for classification, MSE for regression) b.The second measure is the total decrease in node impurities from splitting on the variable, averaged over all trees. For classification, the node impurity is measured by the Gini index. For regression, it is measured by residual sum of squares.
OOB out of bag. bag is part of training set that went into creating the decision tree.OOB estimate is based on testing the forest on data not included in bag.
predicted:

plot(rfn.model,col="black")

library(ggplot2)
library(rattle)

Rattle: A free graphical interface for data science with R.
Version 5.2.0 Copyright (c) 2006-2018 Togaware Pty Ltd.
Type 'rattle()' to shake, rattle, and roll your data.


Attaching package: 'rattle'

The following object is masked from 'package:ranger':

    importance

The following object is masked from 'package:randomForest':

    importance

ggVarImp(rfn.model)

Here are some graphs that visually display the data. As you can see LBXGH the glyhemoglobin is the most import variable to predict if a patient has diabestes. Aslo as we use more random forest tress we get a lower error

rf.predss<-predict(rfn.model,nhanes_test)
#table(rf.predss,nhanes_test$LBXGH)

Gradient Boosting Machine (GBM) algorithm

GBM = is simlar to Adaboost model (1-7 explaination ) with a few changes. GBM = Gradient Descent + Boosting Adaboost model 1. Train decision tree where each observation is assigned an equal weight. 2. After evaluateing first tree we increase the weight of the observation that are difficult to classify and lower weights of observation that are easy to classify. 3. Second tree is grown on weighted data. We want to improve the prediction of the first tree. 4. New model is now Tree 1 + Tree 2 5. Then we compute the classification error from this new 2nd tree ensemble model and grow a 3rd tree to predict the revised residuals. 6. Then we will repeat this process for a specified number of iterations. 7. Subsequent trees help in classifying observation that are not well classified by the preceding trees. 8. The prediction for the final GBM ensemble model is a weighted sum of the predictions made by previous tree models.

How Gradient Boosting Machine works: 1. Gradient boosting identifies the " shortcommings“” of weak learners by gradients in the loss function instead of the high weights used in adaboost. 2. Both high-weight data points and gradients tell us how to improve our model. 3. GBM if tuned properly the performance is often better than other tree based algorithms.

library(tidyverse)
#  Do not change the code in this chunk!
nhanes <- read_csv('nhanes.csv')

Parsed with column specification:
cols(
  .default = col_double(),
  RIAGENDR = col_character(),
  RIDRETH1 = col_character(),
  DR1_300 = col_character(),
  DIQ010 = col_character(),
  SLQ050 = col_character(),
  WHQ030 = col_character()
)

See spec(...) for full column specifications.

nhanes$DIQ010 <- ifelse(nhanes$DIQ010=='Yes', 1,0)
nhanes

# A tibble: 26,193 x 36
   INDFMPIR RIAGENDR RIDAGEYR RIDRETH1 DR1_300 DR1_320Z DR1TALCO DR1TCAFF
      <dbl> <chr>       <dbl> <chr>    <chr>      <dbl>    <dbl>    <dbl>
 1     4.65 Female         44 Non-His… Much l…     193.      0         13
 2     5    Male           70 Non-His… Usual       830.     40.8      260
 3     5    Female         16 Non-His… Much l…     118.      0         71
 4     5    Male           19 Non-His… Usual      1539.      0          0
 5     0.46 Male           21 Other H… Much l…    2577.     36.3       10
 6     1.06 Female         16 Non-His… Usual         0       0        121
 7     1.22 Male           79 Non-His… Usual      2281.     54.3       95
 8     3.03 Female         59 Non-His… Much l…     974       0        249
 9     1.76 Female         27 Mexican… Usual       622.      0         39
10     1.03 Female         44 Other R… Usual      1421.      0        218
# … with 26,183 more rows, and 28 more variables: DR1TCARB <dbl>,
#   DR1TCHOL <dbl>, DR1TFIBE <dbl>, DR1TKCAL <dbl>, DR1TPROT <dbl>,
#   DR1TSFAT <dbl>, DR1TSODI <dbl>, DR1TSUGR <dbl>, DR1TTFAT <dbl>,
#   BMXBMI <dbl>, BPXDI1 <dbl>, BPXPLS <dbl>, BPXSY1 <dbl>,
#   LBDSBUSI <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>, LBDSGLSI <dbl>,
#   LBDSTPSI <dbl>, LBDSTRSI <dbl>, LBDTCSI <dbl>, LBXGH <dbl>,
#   LBXSAPSI <dbl>, LBXSBU <dbl>, LBXSNASI <dbl>, LBXSOSSI <dbl>,
#   DIQ010 <dbl>, SLQ050 <chr>, WHQ030 <chr>

nhanesshort <- select(nhanes, DIQ010,LBXGH, INDFMPIR,INDFMPIR,RIDAGEYR,DR1TCAFF,DR1TFIBE, 
DR1TSODI,DR1TSUGR,BMXBMI,BPXDI1,BPXPLS,LBDSCHSI,LBDSCRSI,LBDSTRSI,LBXGH,LBXSAPSI
)
nhanesshort

# A tibble: 26,193 x 15
   DIQ010 LBXGH INDFMPIR RIDAGEYR DR1TCAFF DR1TFIBE DR1TSODI DR1TSUGR
    <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1      0   6       4.65       44       13      6.4     1426    146. 
 2      1   7.1     5          70      260     20.3     3708    112. 
 3      0   4.7     5          16       71      8.3     1937    137. 
 4      0   4.7     5          19        0     14.3     3289     92.6
 5      0   4.8     0.46       21       10     10.2     2959     77.7
 6      0   5       1.06       16      121      9.7     3090    153. 
 7      0   5       1.22       79       95     30.3     2031    133. 
 8      1   5.8     3.03       59      249      8.7     2006    166. 
 9      0   4.3     1.76       27       39     15.2     4155     76.0
10      0   4.6     1.03       44      218     66       3135    242. 
# … with 26,183 more rows, and 7 more variables: BMXBMI <dbl>,
#   BPXDI1 <dbl>, BPXPLS <dbl>, LBDSCHSI <dbl>, LBDSCRSI <dbl>,
#   LBDSTRSI <dbl>, LBXSAPSI <dbl>

# Total number of rows in the credit data frame
n <- nrow(nhanesshort)

# Number of rows for the training set (80% of the dataset)
n_train <- round(0.8 * n) 

# Create a vector of indices which is an 80% random sample
set.seed(123)
train_nhanes <- sample(1:n, n_train)

# Subset the credit data frame to training indices only
nhanes_train <- nhanesshort[train_nhanes, ]  
  
# Exclude the training indices to create the test set
nhanes_test <- nhanesshort[-train_nhanes, ]

library(gbm)

Loaded gbm 2.1.4

set.seed(1)
gbm_model <- gbm(formula = DIQ010 ~ ., 
                    distribution = "gaussian", 
                    data = nhanes_train,
                    # data = credit_train,
                    n.trees = 1000)
                    
# Print the model object                    
print(gbm_model)

gbm(formula = DIQ010 ~ ., distribution = "gaussian", data = nhanes_train, 
    n.trees = 1000)
A gradient boosted model with gaussian loss function.
1000 iterations were performed.
There were 14 predictors of which 14 had non-zero influence.

summary(gbm_model)

              var    rel.inf
LBXGH       LBXGH 83.6812007
RIDAGEYR RIDAGEYR  3.3535990
LBDSCRSI LBDSCRSI  3.2594781
LBDSCHSI LBDSCHSI  2.3468955
BMXBMI     BMXBMI  2.1443651
DR1TSUGR DR1TSUGR  1.2933787
BPXDI1     BPXDI1  0.8563016
LBDSTRSI LBDSTRSI  0.7250550
DR1TSODI DR1TSODI  0.6341246
LBXSAPSI LBXSAPSI  0.4927267
DR1TCAFF DR1TCAFF  0.4411391
DR1TFIBE DR1TFIBE  0.2874466
BPXPLS     BPXPLS  0.2584364
INDFMPIR INDFMPIR  0.2258530

The above Boosted Machine is a Gradient Boosted Machine which generates 10000 trees and the shrinkage parameter lambda=0.01 which is also a sort of learning rate.
Next parameter is the interaction depth d which is the total splits we want to do.So here each tree is a small tree with only 4 splits.
The summary of the model gives a list of feature importance plot.
In the above list, the top is the most important variable and the last item listed is the least important variable. 5.The 2 most important features which explain the maximum variance in the Data set is RIDAGEYR(age of patient) ,LBDSTRSI (Triglyceride levels), INDFMRIR(Poverty income ratio ).

nhanesgbm<-gbm(DIQ010 ~ . ,data = nhanes_train,distribution = "gaussian",n.trees = 1000,
                  shrinkage = 0.01, interaction.depth = 4)
nhanesgbm

gbm(formula = DIQ010 ~ ., distribution = "gaussian", data = nhanes_train, 
    n.trees = 1000, interaction.depth = 4, shrinkage = 0.01)
A gradient boosted model with gaussian loss function.
1000 iterations were performed.
There were 14 predictors of which 14 had non-zero influence.

summary(nhanesgbm) #Summary gives a table of Variable Importance and a plot of Variable Importance

              var    rel.inf
LBXGH       LBXGH 82.7137393
LBDSCHSI LBDSCHSI  5.2878334
RIDAGEYR RIDAGEYR  3.4907106
DR1TSUGR DR1TSUGR  2.3951225
BMXBMI     BMXBMI  1.4231197
LBDSCRSI LBDSCRSI  1.3783977
BPXDI1     BPXDI1  0.5759549
DR1TCAFF DR1TCAFF  0.5216368
DR1TSODI DR1TSODI  0.5103817
LBDSTRSI LBDSTRSI  0.4607417
LBXSAPSI LBXSAPSI  0.4549195
INDFMPIR INDFMPIR  0.3322628
DR1TFIBE DR1TFIBE  0.2627811
BPXPLS     BPXPLS  0.1923983

The above Boosted Model is a Gradient Boosted Model which generates 10000 trees and the shrinkage parameter lambda=0.01 which is also a sort of learning rate.
Next parameter is the interaction depth d which is the total splits we want to do.So here each tree is a small tree with only 4 splits.
The summary of the Model gives a feature importance plot.In the above list is on the top is the most important variable and at last is the least important variable. 3.The 2 most important features which explain the maximum variance in the Data set is RIDAGEYR(age of patient) ,DRITCAFF (caffeine intake), BPXPLS(60 sec pulse ).
In the Summary table the Rel. inf is the relavant influence number for each variable.This number measure and quantifies how useful certain variables were in the training model.

pred <- predict(object = gbm_model,  
                newdata = nhanes_test, n.trees = 1000)  

gbm_rmse <- sqrt(mean((pred - nhanes_test$DIQ010) ^ 2))
gbm_rmse

[1] 0.2364671

Here the predict function is being used. When using the predict function you need to specify how many trees you need.
Here I used the same numbers of trees as the gbm model 1000 but this might not be the optimal number to be used in the predict function.

#set.seed(4933)

#nhanescontrol <- round(method = 'cv', number = 5, summaryFunction=defaultSummary)
#train_grid <- expand.grid( n.trees = seq(50,1000,50), interaction.depth = c(30), shrinkage = c(0.1), n.minobsinnode = 10)

#gbm_model3 <- train(DIQ010 ~ ., data=nhanesshort, method = 'gbm', trControl=train_control,tuneGrid=train_grid,metric='RMSE',maximize=FALSE)

# Train a 10000-tree GBM model
set.seed(1)
credit_model <- gbm(formula = DIQ010 ~., 
                    distribution = "bernoulli", 
                    data = nhanes_train,
                    n.trees = 100)
                    
# Print the model object                    
print(credit_model)

gbm(formula = DIQ010 ~ ., distribution = "bernoulli", data = nhanes_train, 
    n.trees = 100)
A gradient boosted model with bernoulli loss function.
100 iterations were performed.
There were 14 predictors of which 7 had non-zero influence.

# summary() prints variable importance
summary(credit_model)

              var     rel.inf
LBXGH       LBXGH 92.79777697
RIDAGEYR RIDAGEYR  3.28117841
LBDSCHSI LBDSCHSI  1.19726185
LBDSCRSI LBDSCRSI  1.07420319
DR1TSUGR DR1TSUGR  0.82691541
BMXBMI     BMXBMI  0.78842423
LBXSAPSI LBXSAPSI  0.03423993
INDFMPIR INDFMPIR  0.00000000
DR1TCAFF DR1TCAFF  0.00000000
DR1TFIBE DR1TFIBE  0.00000000
DR1TSODI DR1TSODI  0.00000000
BPXDI1     BPXDI1  0.00000000
BPXPLS     BPXPLS  0.00000000
LBDSTRSI LBDSTRSI  0.00000000

library(gbm)
cor(nhanesshort$DIQ010,nhanesshort$BPXPLS)#negetive correlation coeff-r

[1] 0.0338967

cor(nhanesshort$DIQ010,nhanesshort$LBXGH)#positive correlation coeff-r

[1] 0.5808716

Here you can see that BPXPLS variable has a negative correlation with 3% correlation with with having Diabetes. While LBXGH the value of glycohemoglobin % has a positive correlation with 58% correlation with having Diabetes

#Plot of Response variable with lstat variable
plot(gbm_model,i="BPXPLS")

#Inverse relation with lstat variable

plot(gbm_model,i="LBXGH")

#as the average number of rooms increases the the price increases

AT LBXGH 6.5% above we get a positive correlation to Diabetes. At BPXPLS around 45 we get a negative correlation to Diabetes.

n.trees = seq(from=10 ,to=10000, by=100) #no of trees-a vector of 100 values 

#Generating a Prediction matrix for each Tree
predmatrix<-predict(gbm_model,nhanes_train,n.trees = n.trees)

Warning in predict.gbm(gbm_model, nhanes_train, n.trees = n.trees): Number
of trees not specified or exceeded number fit so far. Using 10 110 210 310
410 510 610 710 810 910 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
1000 1000 1000 1000 1000.

dim(predmatrix) #dimentions of the Prediction Matrix

[1] 20954   100

#Calculating The Mean squared Test Error
test.error<-with(nhanes,apply( (predmatrix-DIQ010)^2,2,mean))

Warning in predmatrix - DIQ010: longer object length is not a multiple of
shorter object length

head(test.error) #contains the Mean squared test error for each of the 100 trees averaged

       10       110       210       310       410       510 
0.1212259 0.1556358 0.1592422 0.1580783 0.1647385 0.1545224

#Calculating The Mean squared Test Error
test.error<-with(nhanes,apply( (predmatrix-DIQ010)^2,2,mean))

Warning in predmatrix - DIQ010: longer object length is not a multiple of
shorter object length

head(test.error) #contains the Mean squared test error for each of the 100 trees averaged

       10       110       210       310       410       510 
0.1212259 0.1556358 0.1592422 0.1580783 0.1647385 0.1545224

#Plotting the test error vs number of trees

plot(n.trees , test.error , pch=19,col="blue",xlab="Number of Trees",ylab="Test Error", main = "Perfomance of Boosting on Test Set")
#adding the RandomForests Minimum Error line trained on same data and similar parameters
abline(h = min(test.error),col="red") #test.err is the test error of a Random forest fitted on same data
legend("topright",c("Minimum Test error Line for Random Forests"),col="red",lty=1,lwd=1)

# Since we converted the training response col, let's also convert the test response col
#credit_test$default <- ifelse(credit_test$default == "yes", 1, 0)

# Generate predictions on the test set
preds1 <- predict(object = gbm_model, 
                 newdata = nhanes_test,
                 n.trees = 1000)

# Generate predictions on the test set (scale to response)
preds2 <- predict(object = gbm_model, 
                 newdata = nhanes_test,
                 n.trees = 1000,
                 type = "response")

# Compare the range of the two sets of predictions
range(preds1)

[1] -0.1516679  1.2117125

range(preds2)

[1] -0.1516679  1.2117125

library(pROC)

Type 'citation("pROC")' for a citation.


Attaching package: 'pROC'

The following objects are masked from 'package:stats':

    cov, smooth, var

#Generate the test set AUCs using the two sets of preditions & compare
#auc(actual = nhanes_test$DIQ010, predicted = preds1, auc=TRUE)  #default
#auc(actual = nhanes_test$DIQ010, predicted = preds2, auc=TRUE)  #rescaled

# Optimal ntree estimate based on OOB
ntree_opt_oob <- gbm.perf(object = gbm_model, 
                         method = "OOB", 
                        oobag.curve = TRUE)

OOB generally underestimates the optimal number of iterations although predictive performance is reasonably competitive. Using cv_folds>1 when calling gbm usually results in improved predictive performance.

# Train a CV GBM model
set.seed(1)
nhanes_model_cv <- gbm(formula = DIQ010 ~ ., 
                      distribution = "bernoulli", 
                      data = nhanes_train,
                      n.trees = 10000,
                      cv.folds = 2)
                       
# Optimal ntree estimate based on CV
ntree_opt_cv <- gbm.perf(object = nhanes_model_cv, 
                        method = "cv")

# Compare the estimates                         
print(paste0("Optimal n.trees (OOB Estimate): ", ntree_opt_oob))

[1] "Optimal n.trees (OOB Estimate): 114"

print(paste0("Optimal n.trees (CV Estimate): ", ntree_opt_cv))

[1] "Optimal n.trees (CV Estimate): 334"

gbm.perf() is a function to estimate the optimal number of boosting iterations. (trees to use for gradient boostin model. GBM) 1.Hyperparameter tuining to check for overfitting. Looking at Grid search on subset of the model. 2. Tune number of tuning early stopping. 3. Early stopping is when you stop the training proccess in an iterative algorithm by means of evaluating the model performance on the holdoutset. 4. In this example you we can use it in the gbm out of bag sample, separte validation set or by using cross-validation. It’s best to stop training an iterative model after validation error has decreased and stabilize before the validation error starts to increase dure to overfitting(causeing bias of the model) 5. OOB = computes the out of bag estimate 6. CV = extract the optimial number of iterations using cross validation. 7. The graph shows around 100 iterations is optimal. 8.

# Generate predictions on the test set using ntree_opt_oob number of trees
preds1 <- predict(object = gbm_model, 
                 newdata = nhanes_test,
                 n.trees = ntree_opt_oob)
                  
# Generate predictions on the test set using ntree_opt_cv number of trees
preds2 <- predict(object = gbm_model, 
                 newdata = nhanes_test,
                 n.trees = ntree_opt_cv)   
head(preds1)

[1]  0.031571145  0.017205500  0.091589966 -0.010826062 -0.000960848
[6]  0.107671436

head(preds2)

[1]  0.03076988  0.01702138  0.12900557 -0.01813379 -0.01912493  0.12898503

# Generate the test set AUCs using the two sets of preditions & compare
#auc1 <- auc(actual = nhanes_test$DIQ010, predicted = preds1)  #OOB
#auc2 <- auc(actual = nhanes_test$DIQ010, predicted = preds2)  #CV 

# Compare the estimates                         
print(paste0("Optimal n.trees (OOB Estimate): ", ntree_opt_oob))

[1] "Optimal n.trees (OOB Estimate): 114"

print(paste0("Optimal n.trees (CV Estimate): ", ntree_opt_cv))

[1] "Optimal n.trees (CV Estimate): 334"

# Compare AUC 
#print(paste0("Test set AUC (OOB): ", auc1))                         
#print(paste0("Test set AUC (CV): ", auc2))

# Generate the test set AUCs using the two sets of predictions & compare
#actual <- nhanes_test$DIQ010
#head(actual)
#dt_auc <- auc(actual = actual, predicted = dt_preds)
#bag_auc <- auc(actual = actual, predicted = bag_preds)
#rf_auc <- auc(actual = actual, predicted = rf_preds)
#gbm_auc <- auc(actual = actual, predicted = gbm_preds)

# Print results
#sprintf("Bagged Trees Test AUC: %.3f", bag_auc)
#sprintf("Random Forest Test AUC: %.3f", rf_auc)
#sprintf("GBM Test AUC: %.3f", gbm_auc)

# List of predictions
#preds_list <- list(dt_preds, bag_preds, rf_preds, gbm_preds)

# List of actual values (same for all)
#m <- length(preds_list)
#actuals_list <- rep(list(credit_test$default), m)

# Plot the ROC curves
##rocs <- performance(pred, "tpr", "fpr")
#plot(rocs, col = as.list(1:m), main = "Test Set ROC Curves")
#legend(x = "bottomright", 
 #      legend = c("Decision Tree", "Bagged Trees", "Random Forest", "GBM"),
#       fill = 1:m)

CS x460 Challenge Problems

Phan, Elaine

December 12, 2018

Instructions (read carefully!)

Mandatory Requirements

Grading Criteria

Problem 1

Reading Data set Healthcare

Data Exploration

Summary gives us the values of the min, 1st quantiles, median, mean, 3rd quantiles and max values of each variable on a graph of each variable.

Dplyr data explorations

Here I added a new column or variable called finalcosts where I added the the previous balance and the costs column together to make the finalcost column using mutate function.

The arrange function arranges all the column from least to the most.

People paying the most for healthcare costs are mostly smokers, people with negative prev_balances and are females with 4-3 or 0 children live in southwest, northeast, southeast.

Linear Regression model for Healthcare dataset where test all variables against costs except for the previous balance varoable

1. Here is a linear regression model where we use all variables except previous balance.

Linear Regression on all the features or variables in the Healthcare data set

Box plot graphs of previous balance column vs costs

Looks like the pre_balance variable has a parabola with prices owed and owed to them spreading out from zero to the positive and negative evenly.

Scatter plot of age vs costs

Histogtam of the amount of patients at different age groups

Histogram of number of people at different BMI

Histogram of the number of people paying different costs for healthcare in the dataset

Histogram of the amount of people that carried a range of previous balance for healthcare.

Histogram of number of patients with 0-5 children in thier family.

Boxplot of patients from different regions vs the costs of healthcare

Looks like we have people in southeast paying more for healthcare. The other regions look very close to each other with southwest a little lower in healthcare cost.

Scatter plot showing healthcare cost increases with BMI, vs regions vs gender

looks like male and female both increase their healthcare cost as they have children. It seems like males pay a litte more if they grow their family. The region location of patiensts is hard to read in this graph. But seem like more southeast outliers paying 40K-60K

Scatter plot of BMI vs gender and region

Scatterplot heat map

Doesn’t look like there is a correlation. Most people do seem to have a previous balance of zero.

The male blue line shows that males under twenty pay less for healthcare and after age 23 they start paying the same as females for healthcare. But when males reach their 30’s they start paying more for healthcare cost compated to females.

Linear Regression on all the features or variables in the Healthcare data set

Linear Regression on all the features or variables except gender in the Healthcare data set

Linear Regression the features of body mass in the Healthcare data set vs costs.

Mean Residuals for the Linear regression ran above.

Mod

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e)

Modelpract

MDL

All the Mean Residuals were equal to zero. Meaning that the Residual = Observed value - Predicted value. This says that observed value and predicted values were very close they cancel each other out.

RMSE Root Mean Square Error

Both the RMSE look very high.

The RMSE data seems to say taht Maybe using Linear regression on the data set is not the best model to predict the cost of healthcare.

Here we will split our Healthcare dataset in to a Training and Testing set to test out our Linear regression model and see if we can train our model and test it to see how accuarte it can predict the cost of healthcare.

Spliting Data into train and test set with caTools

Here we set a seed so the training set and test set can be reproducible. Otherwise it would be random and we can’t reproduce the data for practice.

Residual plot to determine the random noise of the model

Scatterplot looking at the BMI vs Cost and filtering the outliers with body mass greater than 35

Here is the actual and predicted cost of healthcare cost for the training samples using the linear regression model.

There shows a small correlation between ages vs costs of healthcare and BMI vs cost of healthcare.

There shows a small correlation between ages vs costs of healthcare and BMI vs cost of healthcare.

Calculating the Residual Mean

plot out the residuals:

Classification and Regression Tree model for the Healthcare data set to determine cost of healthcare.

Tree model maybe a better model to predict and determine the cost of healthcare.

Model interpretability is makes predictions easier in Tree Classification

Model performance of trees have superior performance compared to other ML algorithm.

Here we look at how smokers effect on the price of healthcare cost.

Here we look at the different region of patients paying for healthcare costs.

Here is a classification on region an body mass.

This Regression tree is looking at the Age of the patients in the model.

This Regression tree is looking at the BMI of the patients in the model.

This Regression tree is looking at the number of children patient’s have in the model.

This Regression tree is looking at the previous balance of the patients in the model.

how many rows are in the data

Follow down the Tree:

Slit to Training/Testing/Validation with three sets for Regression Tree

Training with Regression Tree

Predict the cost for all the people in the test set Evaluate model based on test set RMSE Room Mean Square Error.RMSE tells us approximately how far away our predictions are from the true values

Tuning model: Tune model using prune() function by finding best ‘CP’ complexity parameter

Generate grid of hyperparameter values uinge expand.grid() to generate grid of maxdepth and minsplit values

Generate grid models

Evaluate the grid

After the Hyperparameter the best fit model for the Regression tree Predicts that the predicted cost for Healthcare is $3910.80

Problem 2

glycohemoglobin % above 6.5 your prediabetic

Train Test split

Random Forest